Question

an integer is chosen at a random between 1 to 100 find the probability of getting a number divisible by 7 and not divisible by 7​

Answer 1

Step-by-step explanation:

Number of integers between 1 and 100 : 2, 3 , 4, 5 , .....99

so, sample space { or total outcomes } = 98

So, you can say total number of sample space , n(S) = 98

Now , numbers , which are divisible by 7 are : 7 , 14 , 21 , 28, 35 , 42 , 49, 56, 63 ,70, 77 , 84,91

So, total number which are divisible by 7 = 123

So, number of possible event , n(E ) = 13

Now, probability that it is divisible by 7 , P(E) = n(E)/n(S) = 13/98

P(divisible by 7) = 13/98

Probability that it is not divisible by 7 , P(E') = 1 - probability that is is divisible by 7,P(E)

E.g., P( not divisible by 7) = 1 - 13/98 = 85/98

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Answer 2

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Number of integers between 0 and 100 = n(S) = 99

(i) Let E be the event ‘integer divisible by 7’

Favourable outcomes to the event E = 7, 14, 21,…., 98

Number of favourable outcomes = n(E) = 14

Probability = P(E) = n(E)/n(S) = 14/99

(ii) Let F be the event ‘integer not divisible by 7’

Number of favourable outcomes to the event F = 99 – Number of integers divisible by 7

= 99-14 = 85

Hence, the required probability = P(F) = n(F)/n(S) = 85/99

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