A dice is rolled twice. Find the probability that
(i)5 will not come up either time
(ii)5 will come up exactly one time
Answers
Answer:
Step-by-step explanation:
SOLUTION :
Given : A dice is rolled twice .
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 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 exactly one time
Favorable outcomes (5 will come up exactly one time) : {(1, 5) (2, 5) (3, 5) (4, 5) (5, 1) (5, 2) (5, 3) (5, 4) (5, 6) (6, 5)}
Number of favorable outcomes = 10
Probability ,P(E2) = Number of favourable outcomes / total number of outcomes
P(E2) = 10/36 = 5/18
Hence, the Probability that 5 will come up exactly one time , P(E2) = 5/18
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Answer:
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