Question

In throwing a dice find the probability of following events.

(i) Appear a prime number

(ii) appear 1 or less than 1

(iii) appear number less than 6.

Answer 1

In throwing a dice, obtained sample spapce

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

(i) Event E, appear a prime number

then E = {2, 3, 5}

Thus n(E) = 3

Then probability of event E

P(E) = n(E)/n(S) 

= 3/6 = 1/2

Thus, probability to get a prime number is = 1/2

(ii) Event to get number 1 or less than 1

B = {1}

Then n(B) = 1

Thus, probability to get 1 or less than 1

P(B) = n(B)/n(S) = 1/6

Thus, probability to get no. 1 or less than 1 = 1/6

(iii) Event to appear no. less than 6

D = {1,2, 3,4,5}

then n(D) = 5

Then, probability to appear no. less than 6.

P(D) = n(D)/n(S) = 5/6

Thus, probability to get number less than 6 = 5/6