If the mean and variance of a binomial distribution are \(\frac{10}{3}\) and \(\frac{10}{9}\) respectively, then the probability of having at least one success is
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- \(\frac{242}{243}\)
- \(\frac{32}{243}\)
- \(\frac{31}{243}\)
- \(\frac{211}{243}\)
The Correct Option is A
Solution and Explanation
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Self-study helps students to build confidence in learning. It boosts the self-esteem of the learners. Recent surveys suggested that close to 50% of learners were self-taught using internet resources and upskilled themselves.
A student may spend 1 hour to 6 hours in a day in upskilling self. The probability distribution of the number of hours spent by a student is given below:
\[ P(X = x) = \begin{cases} kx^2, & \text{for } x = 1, 2, 3, \\ 2kx, & \text{for } x = 4, 5, 6, \\ 0, & \text{otherwise.} \end{cases} \]
where \( x \) denotes the number of hours. Based on the above information, answer the following questions:
(i) Express the probability distribution given above in the form of a probability distribution table.
(ii) Find the value of \( k \).
(iii)(a) Find the mean number of hours spent by the student.
(iii)(b) Find \( P(1 < X < 6) \).- CBSE Class XII - 2024
- Mathematics
- Probability Distribution
- 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.
- CBSE Class XII - 2024
- Mathematics
- Probability Distribution
Self-study helps students to build confidence in learning. It boosts the self-esteem of the learners. Recent surveys suggested that close to 50% learners were self-taught using internet resources and upskilled themselves. A student may spend 1 hour to 6 hours in a day upskilling self. The probability distribution of the number of hours spent by a student is given below:
\[ P(X = x) = \begin{cases} kx^2 & {for } x = 1, 2, 3, \\ 2kx & {for } x = 4, 5, 6, \\ 0 & {otherwise}. \end{cases} \]
Based on the above information, answer the following:
- CBSE Class XII - 2024
- Mathematics
- Probability Distribution
Questions number 19 and 20 are Assertion and Reason-based questions. Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C), and (D) as given below.
(A) Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of the Assertion (A).
(B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
(C) Assertion (A) is true, but Reason (R) is false.
(D) Assertion (A) is false, but Reason (R) is true.- CBSE Class XII - 2024
- Applied Mathematics
- Probability Distribution
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