Question

Twelve cards are numbered from 1 to 12 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? SHOW WORK

Answer 1

0.1136

Explanation:

Total number of possible outcomes:

You start with 12 cards in the box. After selecting the first card, 11 cards remain. Total number of possible outcomes is 12 x 11 = 132.

Number of favorable outcomes:

There are six even numbers (2, 4, 6, 8, 10, 12) among the twelve cards.

To find the number of ways to choose two even numbers out of six use the formula for combinations:

C(n, r) = n! / (r!(n-r)!)

n = the total number of items = 6

r = the number of items to be chosen = 2

C(6, 2) = 6! / (2!(6-2)!)

= 6! / (2! * 4!)

= (6 * 5 * 4!) / (2! * 4!)

= (6 * 5) / (2 * 1)

= 15

Therefore, the number of favorable outcomes = 15

Probability = Number of favorable outcomes / Total number of possible outcomes

= 15 / 132

≈ 0.1136