please help At the local Quicki Mart Gas Station, two employees review the breakdown of last month's sales data, as follows:Assuming that this distribution is true for future purchases, if a customer pulls into the station and they are drivingFruck, what's the probability that they will buy regular gas?70.02%31.07% of all sales were made to trucks70.02% of all sales were for regular gas20.45% of all sales were for mid-grade gas0% of the sales of premium gas were for trucks.. Note that there's only 3 types of gas; regular, mid-grade and premium.74.39% of the sales of mid-grade gas were not for trucks1.07% O 70.02%Assuming that this distribution is true for future purchases, if a customer pulls into the staa truck, what's the probability that they will buy regular gas?O 31.07%O 83.14%O 44.12%- 31.07% of all sales were made to trucks70.02% of all sales were for regular gas20.45% of all sales were for mid-grade gasO 64.28%0% of the sales of premium gas were for trucks.. Note that there's only 3 types of gas; regular, mid-grade and premium.74.39% of the sales of mid-grade gas were not for trucks

There are 3 types of gases: regular mid-grade and premium. P(T) is the probability that a sale is made to tracks.P(T) = 0.3107P(R) is the probability that a sale is made for regular gas.P(R) = 0.7002P(M) is the probability that a sale is made for mid-grade gas.P(M) = 0.2045P(T|P) is the probability that the sale of premium gas was for the truck.P(T|P) = 0.0P(T'|M) is the probability that the sale of mid-grade gas was not for truck.P(T'|M) = 0.7439A customer pulls into the station and they are driving a truck The probability that they will buy regular gas is denoted by P(R|T).Now calculate the probability P(T|R) denotes the probability that the sale of regular gas was for the truck.P(T) = P(T|R)P(R)+P(T|M)P(M)+P(T|P)P(P) = P(T|R) 0.7002+(1-P(T'|M)0.2045+0P(P) ..............use P(A) = 1-P(A') for mid-grade gas = P(T|R) 0.7002+(1-0.7439)0.2045 = P(T|R) 0.7002+0.25610.2045 = P(T|R) 0.7002+0.0524P(T|R) 0.7002 =P(T)-0.0524 P(T|R) 0.7002 =0.3107-0.0524............P(T) =0.3107P(T|R) 0.7002 =0.2583P(T|R) =P(T|R) = 0.3689We know that P(A|B) =P(T|R)= .........equ(1)and P(R|T) =.........equ(2)now taking the ratio equ(2)/equ(1)If a customer pulls into the station and they are driving a truck the probability that they will buy regular gas is 0.8314 i.e.83.14% Hence option (c) is correct.If a customer pulls into the station and they are driving a truck the probability that they will buy regular gas is 83.14% Hence option (c) is correct.