Question

At a self-service gas station, 40% of customers pump regular gas, 35% pump midgrade, and 25% pump premium gas. Of those who pump regular, 30% pay at least $30. Of those who pump midgrade, 50% pay at least $30. And of those who pump premium, 60% pay at least $30. (a) What is the probability that the next customer pumps premium gas and pays at least $30? (b) What is the probability that the next customer pays at least $30? (c) What fraction of customers who pay at least $30 pump premium gas?

Answer 1

Answer:

0.150,0.595

Step-by-step explanation:

Given that at a self-service gas station, 40% of customers pump regular gas, 35% pump midgrade, and 25% pump premium gas. Of those who pump regular, 30% pay at least $30. Of those who pump midgrade, 50% pay at least $30. And of those who pump premium, 60% pay at least $30.

               Regular gas          Midgrade         Premium gas      Total

Percent      40                            35                     25                   100

atleast 30   30%                         50%                 60%

a) The   probability that the next customer pumps premium gas and pays at least $30

=$0.25*0.60\\=0.150$

b)        the probability that the next customer pays at least $30

= P(regular and pays atleast 30%)+P(premium and pays atleast 30%)+P(midgrade and       pays atleast 30%)

=$0.40*0.30+0.35*0.50+0.25*0.60\\=0.12+0.175+0.30\\=0.595$