Question

A bag contains 20 balls. The ratio of red to blue balls is 3:7. A ball is picked at random and replaced. The bag is shaken, and then a second ball is picked at random.

What is the probability that two red balls are picked?
a) 1/30
b) 3/20
c) 9/400
d) 3/100

Answer 1

The probability of picking two red balls from the bag is 9/100.

Step-by-step explanation:

To find the probability that two red balls are picked from a bag with 20 balls, where the ratio of red to blue balls is 3:7, we can break it down into two steps:

1. Find the probability of picking a red ball on the first draw
2. Find the probability of picking a red ball on the second draw after shaking the bag

Step 1: The probability of picking a red ball on the first draw is 3/10, since there are 3 red balls out of a total of 10 balls that are red or blue. The ratio of red to blue balls does not change after the first draw.

Step 2: The probability of picking a red ball on the second draw after shaking the bag is also 3/10, since there are still 3 red balls out of a total of 10 balls. The first ball that was picked is replaced, so the ratios remain the same.

To find the overall probability, we multiply the probabilities of each step together: P(2 red balls) = (3/10) * (3/10) = 9/100, which is equivalent to answer choice d) 3/100.