4. Solve the following involving probability: A. A classroom of children has 11

Question

4. Solve the following involving probability:

A.

A classroom of children has 11 boys and 20 girls in which five students are chosen at random to do presentations. What is the probability that more boys than girls are chosen?

a) 0.0027

b) 0.0388

c) 0.2234

d) 0.1872

e) 0.2261

f) None of the above.

B.

A toy manufacturer inspects boxes of toys before shipment. Each box contains 19 toys. The inspection procedure consists of randomly selecting three toys from the box. If one or more of the toys are defective, the box is not shipped. Suppose that a given box has two defective toys. What is the probability that it will be shipped?

a) 0.5201

b) 0.0175

c) 0.7018

d) 0.5635

e) 0.2982

f) None of the above.

Explanation / Answer

Please note nCr = n! / [(n-r)!*r!]

P(Event) = Number of favourable outcomes/Total Number of outcomes

A) For more boys than girls the favourable options are (3B,2G) or (4B,1G) or (5B,0G)

= (11C3 x 20C2) + (11C4 x 20C1) + (11C5 x 20C0) = (165 x 190) + (330 x 20) + (462 x 1) = 38412

The total number outcomes is choosing 5 students out of 31 = 31C5 = 169911

Therefore the required probability = 38412/169911 = 0.2261 (Option e)

(B) Here the box contains 2 defective and 17 non defective items. My favourable outcome is to pick 3 from the 17 non defective and 0 from the 2 defective toys = 17C3 x 2C0 = 680

My total outcomes is picking any 3 toys from the 19 toys = 19C3 = 969

Therefore the required probability = 680/969 = 0.7018 (Option c)

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