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

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

E ⟶ event of getting a prime no.

No. of favourable outcomes = 9 {2, 3, 5, 7, 11, 13, 17, 19, 23}

Probability, P(E) =`"No.of favorable outcomes"/"Total no.of possible outcomes"` =9/25

(`barE`) ⟶ 𝑒𝑣𝑒𝑛𝑡 𝑜𝑓 𝑛𝑜𝑡 𝑔𝑒𝑡𝑡𝑖𝑛𝑔 𝑎 𝑝𝑟𝑖𝑚𝑒 𝑛𝑜.

𝑃(`barE` ) = 1 − 𝑃(𝐸)

= 1 − 9/25 =16/25

Text Solution

Solution : Total set ={1,2,3,4,...,25}=25 This determines size of set<br> Prime numbers is it ={2,3,5,7,11,13,17,19,23}<br> size =9<br> Probability =9/25

Text Solution

Solution : A = {2, 3, 5, 7, 11, 13, 17, 19, 23} <br> `P(A) = (9)/(25)`

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