Data 605 - Discussion 5

Section 1.2, Exercise 10

Let H represent the event that a bill passes the House of Representatives
Let S represent the event that a bill passes the Senate

Probability that a bill passes the house: P(H) = 0.6
Probability that a bill passes the Senate: P(S) = 0.8

Probability that a bill passes the House or Senate: $P(H S) $ = 0.9

Probability that the bill is presented to the President = Probability that the bill passes both the house and the senate: $ P (H S)$

Using the theorem:

$P(H S) $ = P(H) + P(S) - $ P (H S)$

Therefore:

$ P (H S)$ = P(H) + P(S) - $P(H S) $

$ P (H S)$ = 0.6 + 0.8 - 0.9

Ans <- 0.6 + 0.8 - 0.9

$ P (H S)$ = 0.5

The probability that the bill is presented before the president is 0.5