Question

At a gas station, 50% of the customers use regular gas, 30% use mid-grade gas and 20% use premium gas. Of those customers using regular gas, only 30% fill their tanks. Of those customers using mid-grade gas, 60% fill their tanks, whereas of those using premium, 50% fill their tanks. If the next customer fills the tank, what is the probability that he uses premium gas

Answer 1

The probability is 0.2326 or 23.26%.

Explanation:

The probability that a random customer fills their tank with premium gas is:

`P( prem\ \&\ fill) = 0.2*0.5=0.10`

The probability that a random customer fills their tank is given by:

`P(fill)=P( reg\ \&\ fill)+P( mid\ \&\ fill)+P( prem\ \&\ fill)\\P(fill) = 0.5*0.3+0.3*0.6+0.2*0.5\\P(fill) = 0.43`

Therefore, the probability that a customer used premium gas given that hey have filled their tank is:

`P(prem| fill) = (P( prem\ \&\ fill) )/(P(fill)) \\P(prem| fill) =(0.10)/(0.43)=0.2326`

The probability is 0.2326 or 23.26%.