Question

Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than 4. What is the probability that it is an even number?

Answer 1

Let S = {1, 2, 3, …, 10}

n(S) = 10

Let A be the event of drawing a number greater than 4.

Then A = {5, 6, 7, 8, 9, 10}

n(A) = 6

∴ P(A) = `("n"("A"))/("n"("S")) = 6/10`

Let B be the event of getting a even number.

Then B = {2, 4, 6, 8, 10}

Now A ∩ B = {6, 8, 10}

n(A ∩ B) = 3

∴ P(A ∩ B) = `3/10`

We have to find P`("B"/"A")`

P`("B"/"A") = ("P"("A" ∩ "B"))/("P"("A")) = (3/10)/(6/10) = 3/6 = 1/2`