Question

Find the probability that a number selected from the number 1 to 25 is not a prime number when each of the given numbers is equally likely to be selected.

Answer 1

SOLUTION :  

Given : Numbers from 1 to 25

Total number of outcomes = 25

Let E = Event of getting a not prime number .

Numbers which is not a prime number are = 1, 4, 6, 8,9 10,12, 14, 15, 16,18, 20, 21, 22, 24, 25

Number of outcome favourable to E = 16

Probability (E) = Number of favourable outcomes / Total number of outcomes

P(E) = 16/25  

Hence, the required probability of getting a not prime number , P(E) = 16/25 .

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Answer 2

Hi there!
Here's the answer:

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Given,
A number is selected from numbers 1 - 25

Let S be Sample space
n(S) - No. of total possible outcomes when a number is selected from 25 numbers
n(S) = 25C1

Let E be Event that the number selected is not a prime

Let E' be the Event that the number selected is a Prime
E' = {Prime No.s from 1 - 25}
E' = {2, 3, 5, 7, 11, 13, 17, 19, 23}

No. of favourable outcomes for occurrence of Event E', n(E') = 9

n(E) + n(E') = n(S)
=> n(E) + 9 = 25
=> n(E) = 16

No. of Favorable outcomes for occurrence of Event E, n(E) = 16
[E = {1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25}


Probability = $\frac{No.\: of\: Favorable\: outcomes}{No.\: of\: Total\: Outcomes}$

P(E) = $\frac{n(E)}{n(S)}$

=> P(E) = $\frac{16}{25}$

•°• Required Probability = $\frac{16}{25}$


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