Question

Calculate the expected value of rolling two die if you win $100 for each 1 tossed and $50 for each 5 tossed.

Answer 1

Here total number of combinations of profit here are

(i) there are two 1 tossed on two roll of die

Total earnings = $ 200

Pr(Two 1 rolled on two die) =1/6 * 1/6 = 1/36

(ii) there are two 5 rolled on two roll of die

Total earnings = $ 100

Pr(Two 5 rolled on two die) = 1/6 * 1/6 = 1/36

(iii) there is 1 on one die and 5 on other die

Total earnings = $ 100 + $ 50 = $ 150

Pr(1 on one die and 5 on other die) = 2 * (1/6) * (1/6) = 1/18

(iv) There is 1 on one die and some other number than 1 or 5 on the other die

Total earnings = $ 100

Pr(1 on one die and other than 1 or 5 on the other die) = 2 * (1/6) * (4/6) = 8/36

(v) There is 5 on one die and some number other than 1 or 5 on the other die

Total earnings = $ 50

Pr(5 on one die and other than 1 or 5 onn the other die) = 2 * (1/6) * (4/6) = 8/36

(iv) there is neither 1 not 5 on any die

Total earnings = 0

Pr(neither 1 nor 5 on any die) = (4/6) * (4/6) = 16/36

so here expected earnings =

= 0 * 16/36 + 50 * 8/36 + 100 * 8/36 + 150 * 2/36 + 100 * 1/36 + 200 * 1/36 = $50