Available Questions 39 found Page 1 of 2
Standalone Questions
#1471
Mathematics
Probability
VSA
UNDERSTAND
2025
AISSCE(Board Exam)
Competency
2 Marks
In a village of 8000 people, 3000 go out of the village to work and 4000 are women. It is noted that 30% of women go out of the village to work. What is the probability that a randomly chosen individual is either a woman or a person working outside the village?
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#1470
Mathematics
Probability
VSA
REMEMBER
2025
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
10 identical blocks are marked with '0' on two of them, '1' on three of them, '2' on four of them and '3' on one of them and put in a box. If X denotes the number written on the block, then write the probability distribution of X and calculate its mean.
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#1458
Mathematics
Probability
SA
UNDERSTAND
2025
AISSCE(Board Exam)
Competency
3 Marks
A person is Head of two independent selection committees I and II. If the probability of making a wrong selection in committee I is 0.03 and that in committee II is 0.01, then find the probability that the person makes the correct decision of selection: (i) in both committees (ii) in only one committee.
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#1436
Mathematics
Probability
SA
UNDERSTAND
2025
AISSCE(Board Exam)
Competency
3 Marks
A person has a fruit box that contains 6 apples and 4 oranges. He picks out a fruit three times, one after the other, after replacing the previous one in the box. Find: (i) The probability distribution of the number of oranges he draws. (ii) The expectation of the random variable (number of oranges).
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#1435
Mathematics
Probability
SA
REMEMBER
2025
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
The probability that a student buys a colouring book is 0.7 and that she buys a box of colours is 0.2. The probability that she buys a colouring book, given that she buys a box of colours, is 0.3. Find the probability that the student: (i) Buys both the colouring book and the box of colours. (ii) Buys a box of colours given that she buys the colouring book.
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#1412
Mathematics
Probability
SA
REMEMBER
2025
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
A coin is tossed twice. Let X be a random variable defined as number of heads minus number of tails. Obtain the probability distribution of X and also find its mean.
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#1411
Mathematics
Probability
SA
APPLY
2025
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Find the probability distribution of the number of boys in families having three children, assuming equal probability for a boy and a girl.
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#1391
Mathematics
Probability
SA
REMEMBER
2025
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Two dice are thrown. Defined are the following two events A and B: $A=\{(x,y):x+y=9\}$, $B=\{(x,y):x\ne3\}$ where (x, y) denote a point in the sample space. Check if events A and B are independent or mutually exclusive.
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#1390
Mathematics
Probability
SA
REMEMBER
2025
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
A die with number 1 to 6 is biased such that probability of $P(2)=\frac{3}{10}$ and probability of other numbers is equal. Find the mean of the number of times number 2 appears on the dice, if the dice is thrown twice.
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#1369
Mathematics
Probability
SA
UNDERSTAND
2025
AISSCE(Board Exam)
Competency
3 Marks
For the vacancy advertised in the newspaper, 3000 candidates submitted their applications. From the data it was revealed that two third of the total applicants were females and other were males. The selection for the job was done through a written test. The performance of the applicants indicates that the probability of a male getting a distinction in written test is 0.4 and that a female getting a distinction is 0.35. Find the probability that the candidate chosen at random will have a distinction in the written test.
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#1368
Mathematics
Probability
SA
REMEMBER
2025
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
The probability distribution for the number of students being absent in a class on a Saturday is as follows: X: 0, 2, 4, 5; $P(X)$: p, 2p, 3p, p. Where X is the number of students absent. (i) Calculate p. (ii) Calculate the mean of the number of absent students on Saturday.
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#1348
Mathematics
Probability
SA
REMEMBER
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
The random variable X has the following probability distribution where a and b are some constants: $P(X)$ for X=1 is 0.2, X=2 is a, X=3 is a, X=4 is 0.2, X=5 is b. If the mean $E(X)=3$, then find values of a and b and hence determine $P(X\ge3)$
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#1325
Mathematics
Probability
SA
UNDERSTAND
2024
AISSCE(Board Exam)
Competency
3 Marks
A biased die is twice as likely to show an even number as an odd number. If such a die is thrown twice, find the probability distribution of the number of sixes. Also, find the mean of the distribution.
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#1324
Mathematics
Probability
SA
UNDERSTAND
2024
AISSCE(Board Exam)
Competency
3 Marks
A card from a well shuffled deck of 52 playing cards is lost. From the remaining cards of the pack, a card is drawn at random and is found to be a King. Find the probability of the lost card being a King.
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#1303
Mathematics
Probability
SA
UNDERSTAND
2024
AISSCE(Board Exam)
Competency
3 Marks
E and F are two independent events such that $P(\overline{E})=0\cdot6$ and $P(E\cup F)=0\cdot6$ Find $P(F)$ and $P(\overline{E}\cup\overline{F})$
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#1280
Mathematics
Probability
SA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
A pair of dice is thrown simultaneously. If X denotes the absolute difference of the numbers appearing on top of the dice, then find the probability distribution of X.
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#1259
Mathematics
Probability
SA
UNDERSTAND
2024
AISSCE(Board Exam)
Competency
3 Marks
The chances of P, Q and R getting selected as CEO of a company are in the ratio 4: 1: 2 respectively. The probabilities for the company to increase its profits from the previous year under the new CEO, P, Q or R are 0-3, 0-8 and 0.5 respectively. If the company increased the profits from the previous year, find the probability that it is due to the appointment of R as CEO.
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#912
Mathematics
Probability
SA
APPLY
2023
Competency
3 Marks
There are two coins. One of them is a biased coin such that P (head): P (tail) is 1:3 and the other coin is a fair coin. A coin is selected at random and tossed once. If the coin showed head, then find the probability that it is a biased coin.
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#911
Mathematics
Probability
SA
APPLY
2023
Competency
3 Marks
A pair of dice is thrown simultaneously. If $X$ denotes the absolute difference of numbers obtained on the pair of dice, then find the probability distribution of $X$.
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#910
Mathematics
Probability
SA
APPLY
2023
KNOWLEDGE
3 Marks
31. From a lot of 30 bulbs which include 6 defective bulbs, a sample of 2 bulbs is drawn at random one by one with replacement. Find the probability distribution of the number of defective bulbs and hence find the mean number of defective bulbs.
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Case-Based Questions
CASE ID: #118
Cl: CBSE Class 12
Mathematics
A shop selling electronic items sells smartphones of only three reputed companies A, B and C because chances of their manufacturing a defective smartphone are only 5%, 4% and 2% respectively. In his inventory he has 25% smartphones from company A, 35% smartphones from company B and 40% smartphones from company C.
SUBJECTIVE
APPLY
2025
AISSCE(Board Exam)
Competency
4 Marks
A person buys a smartphone from this shop.
(i) Find the probability that it was defective.
(ii) What is the probability that this defective smartphone was manufactured by company B ?
(i) Find the probability that it was defective.
(ii) What is the probability that this defective smartphone was manufactured by company B ?
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CASE ID: #116
Cl: CBSE Class 12
Mathematics
Based upon the results of regular medical check-ups in a hospital, it was found that out of 1000 people, 700 were very healthy, 200 maintained average health and 100 had a poor health record.
Let $A_1$: People with good health,
$A_2$: People with average health,
and $A_3$: People with poor health.
During a pandemic, the data expressed that the chances of people contracting the disease from category $A_1$, $A_2$ and $A_3$ are 25%, 35% and 50%, respectively.
SUBJECTIVE
APPLY
2025
AISSCE(Board Exam)
Competency
4 Marks
(i) A person was tested randomly. What is the probability that he/she has contracted the disease ?
(ii) Given that the person has not contracted the disease, what is the probability that the person is from category $A_2$ ?
(ii) Given that the person has not contracted the disease, what is the probability that the person is from category $A_2$ ?
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Based on the information provided, here are the step-by-step calculations:Let the events be defined as:$A_1$: Person has good health$A_2$: Person has average health$A_3$: Person has poor health$E$: Person contracts the diseaseFrom the data given:$P(A_1) = \frac{700}{1000} = 0.7$$P(A_2) = \frac{200}{1000} = 0.2$$P(A_3) = \frac{100}{1000} = 0.1$The conditional probabilities of contracting the disease are:$P(E|A_1) = 25\% = 0.25$$P(E|A_2) = 35\% = 0.35$$P(E|A_3) = 50\% = 0.50$(i) Probability that a randomly selected person has contracted the diseaseWe use the Law of Total Probability:$$P(E) = P(E|A_1)P(A_1) + P(E|A_2)P(A_2) + P(E|A_3)P(A_3)$$Substitute the values:$$P(E) = (0.25 \times 0.7) + (0.35 \times 0.2) + (0.50 \times 0.1)$$$$P(E) = 0.175 + 0.07 + 0.05$$$$P(E) = 0.295$$Answer: The probability that the person has contracted the disease is 0.295 (or 29.5%).(ii) Probability that the person is from category $A_2$, given that they have not contracted the diseaseLet $E'$ be the event that the person has not contracted the disease.We need to find $P(A_2|E')$.First, calculate the probability of not contracting the disease, $P(E')$:$$P(E') = 1 - P(E) = 1 - 0.295 = 0.705$$Next, calculate the probability of not contracting the disease given the person is in category $A_2$:$$P(E'|A_2) = 1 - P(E|A_2) = 1 - 0.35 = 0.65$$Now, apply Bayes' Theorem:$$P(A_2|E') = \frac{P(E'|A_2) \cdot P(A_2)}{P(E')}$$Substitute the values:$$P(A_2|E') = \frac{0.65 \times 0.2}{0.705}$$$$P(A_2|E') = \frac{0.13}{0.705}$$$$P(A_2|E') = \frac{130}{705} = \frac{26}{141}$$$$P(A_2|E') \approx 0.1844$$Answer: The probability that the person is from category $A_2$ given they have not contracted the disease is $\frac{26}{141}$ or approximately 0.184.