Suppose you are at a department store looking through the clearance rack, trying

Question

Suppose you are at a department store looking through the clearance rack, trying to find a good deal on a t-shirt in your size. Assume that you remove a shirt from the rack in order to check its size, and then set it aside rather than placing it back on the rack. The rack contains 3 small, 5 medium, 6 large, and 9 extra-large shirts. Find the probability of each event described. (For each problem, assume that the rack begins in its original state.) a) The first two shirts you check are not small. b) The first large shirt you find is the third one you check. c) The first four shirts you check are all extra-large. d) At least one of the first four shirts you check is a medium

Explanation / Answer

Total number of shirts: 3+5+6+9 = 23

(a)

Out of 23 shirts, 20 are not small. So the probability of selecting first not small shirt is

P(first small shirt) = 20/23

After that 22 shirts are remaining out of which 19 are not small so

P(second small shirt | first small shirt) =19/ 22

So the required probability is

P(second small shirt and first small shirt) = P(second small shirt | first small shirt) P(first small shirt) = (19/22) * (20/22) = 07851

(b)

Out of 23 shirts, 6 are large so

P(first large shirt is third you find) = (17/23) * ( 16/22) * (6/21) = 0.1536

(c)

Out of 23 shirts, 14 are extra large so

P(first four are extra large) = (14/23) * ( 13/22) * (12/21)* (11/20) = 0.1130

(d)

The probability that no shirt is medium is

P(out of four no is medium) = (18/23) * ( 17/22) * (16/21)* (15/20) = 0.3456

So the required probability is

P(at least one is medium) =1-P(out of four no is medium) = 0.6544

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---