First slide

Introduction to probability

Question

The probability that a person will get an electric contract is $\frac{2}{5}$ and the probability that he will not get plumbing
contract is $\frac{4}{7}$ .If the probability of getting at least one contract is $\frac{2}{3}$ , the probability that he will get both the contracts is k , then 105k is

Moderate

Solution

$\begin{array}{l} P (E) = \frac{2}{5}; P (F) = P (plumbing) = 1 - \frac{4}{7} = \frac{3}{7} \\ P (E \cup F) = P (E) + P (F) - P (E \cap F) \\ \frac{2}{3} = \frac{2}{5} + \frac{3}{7} - k \Rightarrow k = \frac{17}{105} \end{array}$

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