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Question
A box contains 90 discs, numbered from 1 to 90. If one disc is drawn at random from the box, the probability that it bears a prime number less than 23, is ______.
Options
`7/90`
`9/90`
`1/9`
`10/90`
`4/15`
`4/45`
`8/89`
\[\frac{9}{89}\]
Solution
A box contains 90 discs, numbered from 1 to 90. If one disc is drawn at random from the box, the probability that it bears a prime number less than 23, is `underlinebb(4/45)`.
Explanation:
There are 90 discs numbered from 1 to 90.
∴ Total number of outcomes = 90
The prime numbers less than 23 are 2, 3, 5, 7, 11, 13, 17 and 19.
So, the favourable number of outcomes are 8.
∴ P(disc drawn bears a prime number less than 23) = \[\frac{\text{ Favourable number of outcomes }}{\text{ Total number of outcomes }} = \frac{8}{90} = \frac{4}{45}\]
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