First slide

Theorems of probability

Question

The probability for a contractor to get a road contract is 2/3 and to get a building contract is 5/9. The probability to get atleast one contract is 4/5. The probability to get both the contracts is

Easy

A

$\frac{17}{50}$
B

$\frac{19}{45}$
C

$\frac{16}{39}$
D

$\frac{25}{52}$

Solution

R=Road contract
B= Building contract

$P (R) = \frac{2}{3}, P (B) = \frac{5}{9}, P (R \cup B) = \frac{4}{5}$

$P (R \cap B) = P (R) + P (B) - P (R \cup B)$

                   $= \frac{2}{3} + \frac{5}{9} - \frac{4}{5}$

                   $= \frac{30 + 25 - 36}{45}$

                   $= \frac{19}{45}$

The probability to get both the contracts is $\frac{19}{45}$

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