Class CBSE Class 12 Mathematics Probability Q #1368
KNOWLEDGE BASED
REMEMBER
3 Marks 2025 AISSCE(Board Exam) SA
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.
Prev Next

AI Tutor Explanation

Powered by Gemini

Detailed Solution

Step 1: Calculate p

The sum of all probabilities in a probability distribution must equal 1. Therefore, we have: $p + 2p + 3p + p = 1$

Step 2: Solve for p

Combining the terms, we get: $7p = 1$ Dividing both sides by 7, we find: $p = \frac{1}{7}$

Step 3: Calculate the mean

The mean (or expected value) of a discrete random variable X is given by: $E(X) = \sum [X \cdot P(X)]$

Step 4: Substitute the values

Substituting the given values and the calculated value of $p$, we have: $E(X) = (0 \cdot p) + (2 \cdot 2p) + (4 \cdot 3p) + (5 \cdot p)$ $E(X) = 0 + 4p + 12p + 5p$ $E(X) = 21p$

Step 5: Calculate the final mean

Since $p = \frac{1}{7}$, we substitute this value into the expression for $E(X)$: $E(X) = 21 \cdot \frac{1}{7}$ $E(X) = 3$

Final Answer: p = 1/7, Mean = 3

AI generated content. Review strictly for academic accuracy.

Pedagogical Audit
Bloom's Analysis: This is an REMEMBER question because it requires recalling the basic principles of probability distributions (sum of probabilities equals 1) and the formula for calculating the mean of a discrete random variable.
Knowledge Dimension: CONCEPTUAL
Justification: The question tests the understanding of the concepts of probability distribution and how to calculate the mean from it, rather than just recalling facts or performing a routine procedure.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. It directly relates to the syllabus content on probability distributions and expected value.
Justification: The question is a standard application of the formulas and concepts taught in the probability chapter.

More from this Chapter

SA
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.
SA
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.
SA
Out of two bags, bag I contains 3 red and 4 white balls and bag II contains 8 red and 6 white balls. A die is thrown. If it shows a number less than 3 then a ball is drawn at random from bag I, otherwise a ball is drawn at random from bag II. Find the probability that the ball drawn from one of the bags is a red ball.
SA
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.
SUBJECTIVE
(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 $A_2$ ?
View All Questions