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

Question

Infinity Learn · Accepted Answer

Let Abe the event 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 $$n(A$$∩$$B)=7C1$$. The number of ways of selecting either two even numbers or selecting two odd numbers is $$n(B)=1+8C2$$. ∴ $$P(A/B)=P(A$$∩$$B)P(B)=729=0.24$$

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

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