Answer to Question #145633 in Statistics and Probability for qwerty

Question

2. The probabilities that a service station will pump gas into 0, 1, 2, 3, 4, or 5 or more cars during a certain 30-minute period are 0.03, 0.18, 0.24, 0.28, 0.10, and 0.17, respectively. Find the probability that in this 30-minute period

(a) more than 3 cars receive gas
(b) 2 or 3 cars receive gas
(c) 7 cars receive gas

Answer 1

Let random variable X represent the number of cars that pumped gas during 30 minutes. We have:

$P(X=0)=0.03$

$P(X=1)=0.18$

$P(X=2)=0.24$

$P(X=3)=0.28$

$P(X=4)=0.10$

$P(X\ge5)=0.17$

a) More than 3 cars receive gas:

$P(X>3)=P(X=4)+P(X\ge5)=0.10+0.17=0.27$

b) 2 or 3 cars receive gas:

$P(X=2) orP(X=3)=P(X=2)+P(X=3)=0.24+0.28=0.52$

c)7 cars receive gas:

$P(X\ge5)=0.17$

Answer:

a) 0.27

b) 0.52

c) 0.17