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

The probability that the next customer pumps premium gas and pays at least $30 is 15%. The probability that the next customer pays at least $30 is 49.5%. The fraction of customers who pay at least $30 and pump premium gas is 30.3%.

Step-by-step explanation:

(a) To find the probability that the next customer pumps premium gas and pays at least $30, we need to multiply the two probabilities together. The probability of pumping premium gas is 25% and the probability of paying at least $30 given that they pump premium gas is 60%. Therefore, the probability is:

0.25 * 0.60 = 0.15 or 15%

(b) To find the probability that the next customer pays at least $30, we need to sum up the individual probabilities for each type of gas. The probability of pumping regular gas and paying at least $30 is 30% of 40%, the probability of pumping midgrade gas and paying at least $30 is 50% of 35%, and the probability of pumping premium gas and paying at least $30 is 60% of 25%. Therefore, the probability is:

0.30 * 0.40 + 0.50 * 0.35 + 0.60 * 0.25 = 0.12 + 0.175 + 0.15 = 0.495 or 49.5%

(c) To find the fraction of customers who pay at least $30 and pump premium gas, we need to divide the probability of pumping premium gas and paying at least $30 (0.15) by the probability of paying at least $30 (0.495). Therefore, the fraction is:

0.15 / 0.495 = 0.303 or 30.3%

Answer 2

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`