Find the probability the first is even and the second is odd.

Question

Ten cards are numbered 1 through 10. Two cards are selected (without replacement).

Answer 1

From the given data 10 cards are numbered 1 through 10.

Two are selected with out replacement.

There are 5 even cards and 5 odd cards.

Lets consider the ordered samples.

For the event must choose an ordered sample of 2 from 10 cards : |S| = 10p₂.

There are 5 chances to select the first card as an even and 5 chances to select the second card as an odd.

For the event to select the first card as an even and the second card as an odd : |D| = 5p₁ * 5p₁ .

The probability : P(D) = |D| / |S| = (5p₁ * 5p₁) / 10p₂

_{= (5 * 5) / (10 * 9)}

_{= 5 / 18.}

_{Therefore, the probability the first is even and the second is odd is 5/18.}