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Answer the following about the probability distribution.
In a school, there are 30 teachers in the examination committee. Out of these, 20 never commit any…
In a school, there are 30 teachers in the examination committee. Out of these, 20 never commit any error in their work. Two teachers are selected at random from the committee. The random variable $X$ is the number of selected teachers who never make an error in their work.
Find the probability distribution of this random variable.
Answer
Answer
AI30 teachers: 20 never err and 10 do. Two are selected, $n(S) = {}^{30}C_2 = 435$.
$P(X = 0) = \dfrac{{}^{10}C_2}{435} = \dfrac{45}{435} = \dfrac{3}{29}$
$P(X = 1) = \dfrac{{}^{20}C_1 \cdot {}^{10}C_1}{435} = \dfrac{200}{435} = \dfrac{40}{87}$
$P(X = 2) = \dfrac{{}^{20}C_2}{435} = \dfrac{190}{435} = \dfrac{38}{87}$
| $X$ | 0 | 1 | 2 |
|---|---|---|---|
| $P(X)$ | $\dfrac{3}{29}$ | $\dfrac{40}{87}$ | $\dfrac{38}{87}$ |
From ISC 2025 Improvement Mathematics Paper 1, question 10(ii).
Check your working with the Probability distribution calculator: find k, the mean, variance and standard deviation of a random variable, with the working table.