Question

Twenty-four cards are numbered from 1 to 24 and placed in a box. One card is selected at random

and not replaced. Another card is randomly selected. What is the probability of selecting two even
numbers?

Answer 1

11/46

Explanation:

between 1 and 24 there are 12 even numbers.

the probability of selecting an even number the first time is 12/24 = 1/2

the probability of the second one being an even number without replacement is 11/23

the probability of both being even numbers without replacement is:

1/2 * 11/23

= 11/46

Answer 2

11/46

Explanation:

Given that there are 24 cards numbered 1 - 24

Even Cards = 2,4,6,8,10,12,14,16,18,20,22,24

Odd Cards = 1,3,5,7,9,11,13,15,17,19,21,23

We can see above that in the beginning, we have:

12 odd and 12 even cards (total of 24 cards)

If we draw the first card and it is even,

P(even number on first draw) = 12/24 = 1/2

If the card is not replaced, now we have:

12 odd cards and 11 even cards (total of 23 cards)

If we draw the 2nd card and it is even,

P(even number on second draw) = 11/23

Hence probabliliy of drawing the first even card, not replacing and then drawing another even card

= (1/2) x (11/23)

= 11/46