Two dice are thrown simultaneously what is the probability that

Asked by admin @ 06/08/2021 in Math viewed by 334 People

Two dice are thrown simultaneously. What is the probability that:

(i)5 will not come up on either of them?
(ii)5 will come up on at least one?
(iii)5 will come up at both dice?

Answered by admin @ 06/08/2021

SOLUTION :

Given : Two dice are thrown simultaneously

If we throw two dices then there possible outcomes are as follows:

{(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)}

Total no. of possible outcomes when 2 dice are thrown = 6 x 6 = 36

(i) Let E1 = Event of 5 will not come up on either of them

Favorable outcomes(5 not coming up on either of them) :

{(1, 1) (1, 2) (1, 3) (1, 4) ,(1, 6)

(2, 1) (2, 2) (2, 3) (2, 4) , (2, 6)

(3, 1) (3, 2) (3, 3) (3, 4) , (3, 6)

(4, 1) (4, 2) (4, 3) (4, 4) , (4, 6)

(6, 1) (6, 2) (6, 3) (6, 4) , (6, 6)}

No. of favorable outcomes = 25

Probability ,P(E1) = Number of favourable outcomes / total number of outcomes

P(E1) = 25/36

Hence, the Probability that 5 will not come up on either of them, P(E1) = 25/36

(ii) Let E2 = Event of 5 will come up on at least once

Favorable outcomes (5 will come up on at least once) : {(1, 5) (2, 5) (3, 5) (4, 5) (5, 5) (5, 1) (5, 2) (5, 3) (5, 4) (5, 6) (6, 5)}

Number of favorable outcomes = 11

Probability ,P(E2) = Number of favourable outcomes / total number of outcomes

P(E2) = 11/36

Hence, the Probability that 5 will come up on at least once, P(E2) = 11/36

(iii) Let E3 = Event of getting 5 on both dice

Favorable outcomes(5 on both dice) : {(5, 5)}

Number of favorable outcomes = 1

Probability ,P(E3) = Number of favourable outcomes / total number of outcomes

P(E3) = 1/36

Hence, the Probability that 5 will come on both dice, P(E3) = 1/36

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