A drawer contains 4 black socks, 3 white socks, and 2 red socks. One sock is drawn from the drawer and kept. Then a second sock is drawn from the drawer. What is the probability that both socks are white? Answer options with 5 options A. StartFraction 1 over 6 EndFraction B. StartFraction 1 over 8 EndFraction C. StartFraction 1 over 9 EndFraction D. StartFraction 1 over 12 EndFraction E. StartFraction 2 over 27 EndFraction
Question
A drawer contains 4 black socks, 3 white socks, and 2 red socks. One sock is drawn from the drawer and kept. Then a second sock is drawn from the drawer.
What is the probability that both socks are white?
Answer options with 5 options A. StartFraction 1 over 6 EndFraction
B. StartFraction 1 over 8 EndFraction
C. StartFraction 1 over 9 EndFraction
D. StartFraction 1 over 12 EndFraction
E. StartFraction 2 over 27 EndFraction
Solution
To solve this problem, we need to calculate the probability of drawing a white sock twice in a row.
Step 1: Calculate the total number of socks. We have 4 black socks, 3 white socks, and 2 red socks, so the total is 4 + 3 + 2 = 9 socks.
Step 2: Calculate the probability of drawing a white sock on the first draw. There are 3 white socks out of 9 total socks, so the probability is 3/9 = 1/3.
Step 3: After drawing one white sock, we are left with 2 white socks and 8 total socks. So, the probability of drawing a white sock on the second draw is 2/8 = 1/4.
Step 4: The probability of both events happening (drawing a white sock on the first draw AND drawing a white sock on the second draw) is the product of the probabilities of each event. So, the probability is 1/3 * 1/4 = 1/12.
So, the correct answer is D. StartFraction 1 over 12 EndFraction.
Similar Questions
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