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: \[P(H \cup S) = 0.9 \]
Probability that the bill is presented to the President = Probability that the bill passes both the house and the senate: \[ P (H \cap S)\]
Using the theorem:
\[P(H \cup S) = P(H) + P(S) - P (H \cap S)\]
Therefore:
\[ P (H \cap S) = P(H) + P(S) - P(H \cup S) \]
\[ P (H \cap S) = 0.6 + 0.8 - 0.9 \]
Ans <- 0.6 + 0.8 - 0.9\[ P (H \cap S)\] = 0.5
The probability that the bill is presented before the president is 0.5