What is the probability that a number selected from 1 2 3 25 is a prime number when each of the numbers is equally likely to be?

Question 73 Probability Exercise 13.1

Answer:

Solution:

When one event happens if and only if the other one doesn't, two occurrences are said to be complimentary. The probability of two complementary events add up to one.

Total no. of possible outcomes = 25 {1, 2, 3…. 25}

Let E = Event of getting a prime no.

So, the favourable outcomes are 2, 3, 5, 7, 11, 13, 17, 19, 23

No. of favourable outcomes = 9

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

P(E) = 9/25

The,

$\overline{\mathrm{E}}=\text { Event of not getting a prime }$

$\begin{aligned} &P(\bar{E})=1-P(E) \\ &P(\bar{E})=1-\frac{9}{25} \\ &P(\bar{E})=\frac{16}{25} \end{aligned}$

Therefore, the probability of selecting a number which is not prime is 16/25.

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What is the probability that a number selected from the numbers 1,2,3, …, 20 is a prime number, where each of the given numbers is equally likely to be selected?

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