Question

If two dice are rolled, then find the probability of getting the product of face value 6 or the difference of face values 5

Answer 1

Sample space = {(1, 1), (1, 2), (1, 3), (1, 4),(1, 5), (1, 6), (2, 1),(2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

n(S) = 36

(i) Let A be the event of getting product of face value 6.

A = {(1, 6), (2, 3), (3, 2) (6, 1)}

n(A) = 4

P(A) = `("n"("A"))/("n"("S")) = 4/36`

(ii) Let B be the event of getting difference of face value is 5.

B = {(6, 1)}

n(B) = 1

P(B) = `("n"("B"))/("n"("S")) = 1/36`

A ∩ B = {(6, 1)}

n(A ∩ B) = 1

P(A ∩ B) = `("n"("A" ∩ "B"))/("n"("S")) = 1/36`

P(A ∪ B) = P(A) + P(B) − P(A ∩ B)

= `4/36 + 1/36 - 1/36`

= `4/36`

= `1/9`

The probability is `1/9`