1.

A two-digit number is formed with digits 2,3,5,7,9 without repetition. What is the probability that the number formed is (1) an odd number? (2) a multiple of 5 ?

Answer» Correct Answer - (1) `(4)/(5)`
(2) `(1)/(5)`
The sample space is
`S={23,25,27,29,32,35,37,39,52,53,57,59,72,73,75,79,92,93,95,97)`
`n(S)=20`
(1) Let A be the event that two-digit odd numbers are formed.
`Then,A={23,25,27,29,35,37,39,53,57,59,73,75,79,93,95,97)`
`thereforen(A)=16`
`P(A)=(n(A))/(n(S))=(16)/(20)=(4)/(5)`
`thereforeP(A)=(4)/(5).`
Let B be the event that the two- digit number is a multiple of five.
Then, B={25,35,75,95}
`thereforen(B)=4`
`P(B)=(n(B))/(n(S))=(4)/(20)=(1)/(5)`
`thereforeP(B)=(1)/(5).`


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