Answer:
\(\frac{1}{16}\)
Step-by-step explanation:
Given : The number of marbles of different colors stored in a hat is listed below:
8 red marbles
10 green marbles
6 blue marbles
To Find: What is the probability that Tessa takes out a blue marble in both draws?
Solution:
8 red marbles
10 green marbles
6 blue marbles
Total Marbles = 8+10+6= 24
Probability of getting blue marble on first draw = \(\frac{\text{No. of blue marbles}}{\text{Total no. of marbles}}\)
Probability of getting blue marble on first draw = \(\frac{6}{24}\)
Now the marble is replaced
Probability of getting blue marble on second draw = \(\frac{\text{No. of blue marbles}}{\text{Total no. of marbles}}\)
Probability of getting blue marble on second draw = \(\frac{6}{24}\)
So, probability of getting blue marble on both the draws = \(\frac{6}{24} \times \frac{6}{24}\)
= \(\frac{36}{576}\)
= \(\frac{1}{16}\)
Hence the probability that Tessa takes out a blue marble in both draws is \(\frac{1}{16}\)
