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A box contains 90 cards bearing a number...

A box contains 90 cards bearing a number from 1 to 90. Find the probability that the card drawn bears
(i) a two-digit number
(ii) a perfect square number.

Text Solution

Verified by Experts

The correct Answer is:
`(i)9/10" "(ii)1/10.`
The total number of cards are 90.
`thereforeS={1,2,3,…,89,90}" "thereforen(S)=90`
(i) Let A be the event that the card drawn is a two-digit number.
Then `A={10,11…,89,90}`
`thereforen(A)=81" "[90-9` (one-digit number)=81]
`P(A)=(n(A))/(n(S))" "thereforeP(A)=81/90=9/10`
(ii) Let B the event that the card drawn is a perfect square number.
Then `B={1,4,9,16,25,36,49,64,81}" "thereforen(B)=9`
`P(B)=9/90=1/10`
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