Question

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

Prime numbers are the positive integers, which are only divisible by itself and 1.

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◗ Prime numbers upto 25 are:

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$\star\:\boxed{\sf{1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀

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$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\;that\; :}}$

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• Probability is an assumption that how likely the event will occur.

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◗ To find the probability of any event, formula is given by:

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$\bf{\dag}\quad\large\boxed{\sf P_{\:(Event)} = \dfrac{Number\; of \: favourable\; outcomes}{Total \; number \; of \; outcomes}}$

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Here,

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• Number of favourable outcomes are 16

• And, total number of outcomes are 25

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Therefore,

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$:\implies\sf P_{\:(Probability)} = \bigg(\dfrac{16}{25}\bigg)$

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$\therefore{\underline{\sf{Hence, \: the \; probability \; is \; \bf{\dfrac{16}{25}}.}}}$

Answer 2

Given:

A number is selected at random from the numbers 1 to 25.

Each of the given numbers is equally likely to be selected.

To Find:

Probability that the number is not a prime number.

Solution:

Required Sample space of the following event ( Non- prime numbers between 1 to 25 )

=> 1, 4, 6, 8,9 10,12, 14, 15, 16,18, 20, 21, 22, 24, 25

Number of Favourable Outcomes = 16

Total number of outcomes = 25

Now as we know

Probability of an event =

$\star\;\boxed{\sf{\pink{\dfrac{ Favourable\; number\;of\; outcomes}{Total\; number\;of\; outcomes}}}}$

Probability = 16/25

Hence, probability that the number is not a prime number is 16/25.