A drawer of socks contains three black socks, four blue socks, and three grey socks. Two socks are chosen at random without replacement. Based on the given information, answer the following questions (12 and 13). What is the probability that a black pair is chosen ? Enter the answer correct to two decimal places.
Question
A drawer of socks contains three black socks, four blue socks, and three grey socks. Two socks are chosen at random without replacement. Based on the given information, answer the following questions (12 and 13). What is the probability that a black pair is chosen ? Enter the answer correct to two decimal places.
Solution
To find the probability of drawing a black pair of socks, we first need to find the total number of ways to draw 2 socks out of 10 (3 black + 4 blue + 3 grey = 10 socks). This can be calculated using the combination formula: C(n, r) = n! / [r!(n-r)!], where n is the total number of items, r is the number of items to choose, and "!" denotes factorial.
The total number of ways to draw 2 socks out of 10 is C(10, 2) = 10! / [2!(10-2)!] = 45.
Next, we need to find the number of ways to draw 2 black socks out of 3. This is calculated as C(3, 2) = 3! / [2!(3-2)!] = 3.
The probability of drawing a black pair is then the number of ways to draw 2 black socks divided by the total number of ways to draw 2 socks. So, the probability is 3/45 = 0.067, or 6.7% when expressed as a percentage.
So, the probability that a black pair is chosen is 0.07 (rounded to two decimal places).
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