A pair of numbers is picked up randomly (without replacement) from the set {1,2,3,5,7,11,12,13,17,19}. The probability that the number 11 was picked g

Question

A pair of numbers is picked up randomly (without replacement) from the set {1,2,3,5,7,11,12,13,17,19}. The probability that the number 11 was picked g

A pair of numbers is picked up randomly (without replacement) from the set {1,2,3,5,7,11,12,13,17,19}. The probability that the number 11 was picked given that the sum of the numbers was even is nearly `0. 1` b. `0. 125` c. `0. 24` d. `0. 18`

Monjur Alahi

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2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - C
Let A be the evetn that 11 is picked and B be the event that sum is even. The number of ways of selecting 11 along with one more odd number is n `(AnnB)=""^(7)C_(1).`
The number of ways of selecting either two even numbers or selecting two odd numbers is `n(B)=1+""^(8)C_(2).`
`P(A//B)=(P(AnnB))/(P(B))=7/29=0.24`