First slide

Theorems of probability

Question

The probability for a contractor to get a road contract is $\frac{3}{4}$ and to get a building contract is $\frac{5}{8}$ . The probability to get atleast one contract is $\frac{7}{8}$ . The probability to get both the contracts is

Moderate

A

$\frac{17}{50}$
B

$\frac{1}{2}$
C

$\frac{16}{39}$
D

$\frac{1}{3}$

Solution

$\begin{matrix} p (A \cap B) = p (A) + p (B) - p (A \cup B) \\ = \frac{3}{4} + \frac{5}{8} - \frac{7}{8} = \frac{1}{2} \end{matrix}$

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