The sale bin in a clothing store contains an assortment of t-shirts in different sizes.There are 6 small,8 medium,and 5 large shirts.Alan is looking for a large shirt.He starts grabbing shirts one at a time and checking the size.After he checks each shirt,he leaves it outside the bin.What is the probability that at least one of the first four shirts he checks is a large?
A)0.295
B)0.117
C)0.742
D)0.705
E)0.258

Question

Quizplus · Accepted Answer

The probability of at least one large shirt in the first four picks is easier to calculate by finding the complement (none of the first four shirts are large) and subtracting from 1. The probability of not picking a large shirt in each of the four picks is $\frac{14}{19} \times \frac{13}{18} \times \frac{12}{17} \times \frac{11}{16}$ (since there are 14 non-large shirts out of 19 total initially, then 13 out of 18, and so on). This gives approximately 0.258. Therefore, the probability of at least one large shirt is $1 - 0.258 = 0.742$.

The Sale Bin in a Clothing Store Contains an Assortment