Answer:
P(at least 1 large) = 0.648
P(at least 1 large) = 64.8%
Step-by-step explanation:
We have 7 small shirts, 8 medium shirts and 4 large shirts
Total number of shirts = 7 + 8 + 4 = 19 shirts
The probability that at least one of the first four shirts he checks is a large is given by
P(at least 1 large) = 1 - P(no large)
So first we need to find the probability that the none of the first four shirts he checks are large.
For the first check, there are 15 small and medium shirts and total 19 shirts so,
15/19
For the second check, there are 14 small and medium shirts and total 18 shirts left so,
14/18
For the third check, there are 13 small and medium shirts and total 17 shirts left so,
13/17
For the forth check, there are 12 small and medium shirts and total 16 shirts left so,
12/16
the probability of not finding the large shirt is,
P(no large) = 15/19*14/18*13/17*12/16
P(no large) = 0.352
Therefore, the probability of finding at least one large shirt is,
P(at least 1 large) = 1 - P(no large)
P(at least 1 large) = 1 - 0.352
P(at least 1 large) = 0.648
P(at least 1 large) = 64.8%
