Exercise- Discrete Probability Distributions - 1.2 10

Solution:

Let P(S) denote the probability that a bill passes the Senate; let P(H) denote the probability that a bill passes the House of Representatives.

we have as below:

P(H \(\cup\) S) = P(H) +P(S) − P(H \(\cap\) S)

Solving for P(H\(\cap\)S) yields

P(H \(\cap\) S) = P(H) + P(S) − P(H \(\cup\) S)

Substituting 0.6 for P(H), 0.8 for P(S), and 0.9 for P(H \(\cup\) S) yields

P(H \(\cap\) S) = 0.6 + 0.8 − 0.9 = 0.5

The probability that the next bill presented to the two groups will come before the president is 0.5