Question

1. at the lakeside resort, the probability that a guest room has a view of the lake is 0.24. the probability that a guest room has a queen - size bed is 0.74. let a be the event that the guest room has a view of the lake, and let b be the event that the guest room has a queen - size bed. events a and b are found to be independent of each other. determine the exact probability that a randomly selected guest room has a view of the lake and a queen - size bed. determine the exact probability that a randomly selected guest room has a view of the lake or a queen - size bed.

Explanation:

Step1: Find probability of both events occurring

For independent events A and B, the probability of both A and B occurring is given by $P(A\cap B)=P(A)\times P(B)$.
$P(A) = 0.24$, $P(B)=0.74$. So $P(A\cap B)=0.24\times0.74 = 0.1776$.

Step2: Find probability of either event occurring

The probability of A or B occurring is given by $P(A\cup B)=P(A)+P(B)-P(A\cap B)$.
We know $P(A) = 0.24$, $P(B)=0.74$ and $P(A\cap B)=0.1776$.
So $P(A\cup B)=0.24 + 0.74- 0.1776=0.8024$.

Answer:

The probability that a randomly - selected guest room has a view of the lake and a queen - size bed is $0.1776$. The probability that a randomly - selected guest room has a view of the lake or a queen - size bed is $0.8024$.