n are at a department store looking through the clearance rack, trying to finda

Question

n are at a department store looking through the clearance rack, trying to finda on a t-shirt in your size. Assum eal e that you remove a shirt from the rack in order to check its size, an 3 s ze, and then set it aside rather than placing it back on the rack. The rack contains mall described. (For each a medium,6 large, and 9 extra-large shirts. Find the probability of each event (For each problem, assume that the rack begins in its original state.) a) The first two shirts you check are not small. ) 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

(a)

Small = 3

Medium = 5

Large = 6

Extra large = 9

Total = 23

Selection 1: Not Small

P(Selection 1: Not small) = 20/23 = 0.8696

After selection 1:
Small = 3

Orgers = 19

Total = 22

P(Selection 2: Not small) = 19/22 = 0.8636

So,

P(First 2: Not Small) = 0.8696 X 0.8636 = 0.7510

(b)

P(Selection 1: Not large) = 17/23 = 0.7391

P(Selection 2: Not large) = 16/22 = 0.7272

P(Selection 3: large) = 6/21=0.2857

So,

P(First Large is Third) = 0.7391 X 0.7272 X 0.2857 = 0.1531

(c)

P(Selection 1: Extra large) = 9/23 = 0.3913

P(Selection 2: Extra large) = 8/22 = 0.3636

P(Selection 3: Extra large) = 7/21 = 0.3333

P(Selection 4: Extra large) = 6/20 = 0.3

So,

P(First 4: Extra large) = 0.0142

(d)

P(At least 1 Modium) = 1 - No medium)

P(Selection 1: No Medium) = 18/23 = 0.7826

P(Selection 2: No Medium) = 17/22 = 0.7727

P(Selection 3: No Medium) = 16/21 = 0.7619

P(Selection 4: No Medium) = 15/20 = 0.75

So,

P(No Medium) = 0.3455

So,

P(at least one meduim) = 1 - 0.3455 = 0.6546

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.