Question

A bowl contains 10 red balls and 10 blue balls. A woman selects two balls without replacement. What is the probability that both balls are red?

a) 1/20
b) 1/19
c) 1/18
d) 1/17

Answer 1

The question involves calculating the probability of selecting two red balls without replacement from a bowl with 10 red and 10 blue balls. The correct answer is found by multiplying the probabilities of each draw, leading to the final answer (b) 1/19.

Step-by-step explanation:

The question asks for the probability that both balls selected from a bowl are red. The total number of balls is 20 (10 red and 10 blue). To find the probability of selecting two red balls without replacement, we calculate the probability of selecting one red ball and then another red ball.

For the first red ball, the probability is 10 red balls out of 20 total balls, which simplifies to 1/2. After taking one red ball out, there are 9 red balls left and a total of 19 balls. The probability of selecting a second red ball is now 9 red balls out of 19 total balls, which simplifies to 9/19.

To find the total probability of both events happening in sequence (both balls being red), we multiply their probabilities: (1/2) × (9/19), which equals 9/38. This fraction reduces to 3/19, so the correct answer is (b) 1/19.