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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

User Sach
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1 Answer

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Answer: D: StartFraction 1 over 12 EndFraction.

Step-by-step explanation:To find the probability that both socks drawn are white, we can use the multiplication rule of probability.

The probability of drawing a white sock on the first draw is 3/9 (since there are 3 white socks out of 9 total socks in the drawer).

After the first sock is drawn and kept, there are 8 socks remaining in the drawer, including 2 white socks. So the probability of drawing a white sock on the second draw, given that a white sock was not replaced after the first draw, is 2/8.

Using the multiplication rule, we can find the probability of both events happening (drawing a white sock on the first try and drawing a white sock on the second try):

P(white, then white) = P(white on first draw) × P(white on second draw | white on first draw)

P(white, then white) = (3/9) × (2/8)

P(white, then white) = 1/12

Therefore, the probability that both socks drawn are white is option D: StartFraction 1 over 12 EndFraction.

User Javic
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