A bag contains 16 socks. One sock is chosen at random. The probability of selecting a black, white, or gray sock is 1. The probability of selecting a white sock is 3 4 . Selecting a gray sock is less likely than selecting a black sock. Which statements describe the situation? Highlight all the correct answers. A There are 2 black socks. B There are 12 white socks. C There is at most 1 gray sock. D It is impossible to select a red sock. E It is likely that a black sock is selected.
Question
A bag contains 16 socks. One sock is chosen at random. The probability of selecting a black, white, or gray sock is 1. The probability of selecting a white sock is 3 4 . Selecting a gray sock is less likely than selecting a black sock. Which statements describe the situation? Highlight all the correct answers. A There are 2 black socks. B There are 12 white socks. C There is at most 1 gray sock. D It is impossible to select a red sock. E It is likely that a black sock is selected.
Solution
The correct statements that describe the situation are:
B. There are 12 white socks. This is because the probability of selecting a white sock is 3/4 and since there are 16 socks in total, 3/4 of 16 equals 12.
C. There is at most 1 gray sock. This is because selecting a gray sock is less likely than selecting a black sock. Since the total probability is 1 and the probability of selecting a white sock is 3/4, the combined probability of selecting a black or gray sock is 1/4. If there were more than one gray sock, it would be more likely to select a gray sock than a black sock, which contradicts the given information.
D. It is impossible to select a red sock. This is because the probability of selecting a black, white, or gray sock is 1, which means that all the socks in the bag are either black, white, or gray. Therefore, there are no red socks in the bag.
E. It is likely that a black sock is selected. This is because the probability of selecting a black sock is higher than the probability of selecting a gray sock.
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