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Michael has a drawer with 8 pairs of black socks and 12 pairs of white socks. Without looking he takes a white pair of socks out of the drawer. What is the probability that the next pair he takes out is white?
A 8/20
B 8/19
C 11/20
D 11/19
E 12/19
To find the probability that the next pair of socks Michael takes out is white after already taking one white pair, we need to consider how many socks remain and how many pairs of each color are left.
Initially, Michael has:
– 8 pairs of black socks (16 individual socks)
– 12 pairs of white socks (24 individual socks)
After taking one pair of white socks, the counts are:
– Black socks: 16 (no change)
– White socks: 24 – 2 = 22 (since a pair consists of 2 individual socks)
Now, the total number of individual socks remaining is:
16 (black) + 22 (white) = 38 socks.
The probability that the next pair he takes out is white now depends on how many white pairs are left. Since he took out 1 pair of white socks (2 individual socks), he has:
– Remaining white pairs = 11 pairs (22 individual socks left).
So, the probability that the next pair he takes out is white is:
Number of remaining white socks / Total remaining socks = 22 / 38.
However, since we want to express this in terms of pairs, we need to choose the option that best represents this scenario. The probability of taking one of the remaining pairs of white socks is:
P(next pair is white) = Number of remaining white pairs / Total remaining pairs = 11 / 19.
Therefore, the correct answer is D 11/19.