Question

Two dice are thrown simultaneously. Find the probability of obtaining the sum as 6 or same number on both the dice.

Answer 1

Number of sample points in throwing two dice at a time is n(S) = 36

Let A be a event of the sum being 6

A = {(1, 5), (2, 4), (3, 3), (4, 2), (5, 1)}

P(A)= $\frac{5}{36}$

Let B be a event of getting the same number on both dice.

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

P(B) = $\frac{6}{36}$

A $\cap$ B = {(3, 3)}

P(A $\cap$ B) = $\frac{1}{36}$

P(A $\cup$ B) = P(A)+P(B) – P(A $\cap$ B)

= $\frac{5}{36}$ + $\frac{6}{36}$ – $\frac{1}{36}$

= $\frac{10}{36}$

= $\frac{5}{18}$