Question

Harriet has a bag with eight marbles. It contains 4 blue marbles, 3 red marbles, and 1 green marble. She will take out a marble, write down which one it is, and put it back in the bag.

What is the probability that Harriet will take out a blue marble and then a red one?

Answers

Answer 1

To find the probability that Harriet will take out a blue marble and then a red one (with replacement), we can calculate the probabilities of each individual event and then multiply them together.

1. **Probability of taking out a blue marble**:
- There are 4 blue marbles out of a total of 8 marbles.
- The probability \( P(\text{Blue}) \) is:
\[
P(\text{Blue}) = \frac{4}{8} = \frac{1}{2}
\]

2. **Probability of taking out a red marble**:
- There are 3 red marbles out of a total of 8 marbles.
- The probability \( P(\text{Red}) \) is:
\[
P(\text{Red}) = \frac{3}{8}
\]

3. **Combined probability**:
- The events are independent because Harriet replaces the marble after each draw. Therefore, the probability of both events occurring (taking out a blue marble first and then a red marble) is:
\[
P(\text{Blue and then Red}) = P(\text{Blue}) \times P(\text{Red}) = \frac{1}{2} \times \frac{3}{8} = \frac{3}{16}
\]

Thus, the probability that Harriet will take out a blue marble and then a red one is \( \frac{3}{16} \).