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

ANSWER:-

Numbers from 1 to 25 are (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25) Prime Numbers = 2, 3, 5, 7, 11, 13, 17, 19, 23 Total Prime numbers = 9 Total Numbers = 25 Let x be the event of getting prime numbers P(x)= 9 / 25  

Therefore the probability of getting non-prime number = 1 − 9 / 25 = 16 / 25

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

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.

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Cards bearing non prime numbers are 1,4,6,8,9,10,12,14,15,16,18,20,21,22,24, 25

Total number of cards bearing non-prime numbers = 16

Number of favourable elementary events = 16

We know that , Probability = number of favourable elementary eventsTotal number of elementary events

So, P(getting a card bearing a non prime number) = 1625