a number is selected from the set {1,2,3,....,5}.find the probability that it is a prime number.
Answers
SOLUTION :
Given : Numbers selected from 1 to 35
Total number of outcomes = 35
(i) Let E1 = Event of getting a prime number .
Numbers which is a prime number are = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31
Number of outcome favourable to E1 = 11
Probability (E1) = Number of favourable outcomes / Total number of outcomes
P(E1) = 11/35
Hence, the required probability of getting a prime number , P(E1) = 11/35 .
(ii) Let E2 = Event of getting a number which is a multiple of 7.
Numbers which is a multiple of 7 are = 7, 14, 21, 28, 35
Number of outcome favourable to E2 = 5
Probability (E2) = Number of favourable outcomes / Total number of outcomes
P(E2) = 5/35 = 1/7
Hence, the required probability of getting a multiple of 7 , P(E2) = 1/7 .
(iii) Let E3 = Event of getting a number which is a multiple of 3 & 5
Numbers which is a multiple of 3 & 5 are = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 5, 10, 20, 25, 35
Number of outcome favourable to E3 = 16
Probability (E3) = Number of favourable outcomes / Total number of outcomes
P(E3) = 16/35
Hence, the required probability of getting a multiple of 3 & 5 , P(E3) = 16/35 .
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Answer:
Total numbers - 5
Prime numbers - 3 ( 2 , 3 and 5 )
So probability = 3 / 5