Question

A fair coin is tossed 25 times. What is the probability that at least 1 tail occurs?

a) 1

b) 0.00000075

c) 0.99999923

d) 0.00000003

e) 0.99999997

f) None of the above.

A business organization needs to make up a 5 member fund-raising committee. The organization has 9 accounting majors and 7 finance majors. What is the probability that at most 2 accounting majors are on the committee?

a) 0.0151

b) 0.0048

c) 0.3654

d) 0.0103

e) 0.3606

f) None of the above.

A classroom of children has 17 boys and 19 girls in which five students are chosen at random to do presentations. What is the probability that more boys than girls are chosen?

a) 0.4448

b) 0.0164

c) 0.3249

d) 0.1199

e) 0.4284

f) None of the above.

A toy manufacturer inspects boxes of toys before shipment. Each box contains 9 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) 0.4365

b) 0.0833

c) 0.0714

d) 0.5833

e) 0.4167

f) None of the above.

Answer 1

1.
Probability of at least one tail = 1 - Probability that no tails occurs
= 1 - (1/2)²⁵
= 0.99999997
The correct answer is e. 0.99999997

2.
Probability that at most 2 accounting majors are on the committee = Probability that 0 accounting majors are on the committee + Probability that 1 accounting majors are on the committee + Probability that 2 accounting majors are on the committee

= ( ⁹C₀ * ⁷C₅ ) / ¹⁶C₅ + ( ⁹C₁ * ⁷C₄ ) / ¹⁶C₅ + ( ⁹C₂ * ⁷C₃ ) / ¹⁶C₅

= 0.004807692 + 0.07211538 + 0.2884615

= 0.3653846

The correct answer is c) 0.3654

3.

Probability that more boys than girls are chosen = Probability that at most 2 girls are chosen in 5 students = Probability that 0 girls are chosen + Probability that 1 girls are chosen + Probability that 2 girls are chosen

= ( ¹⁹C₀ * ¹⁷C₅ ) / ³⁶C₅ + ( ¹⁹C₁ * ¹⁷C₄ ) / ³⁶C₅ ​​​​​​​ + ( ¹⁹C₂ * ¹⁷C₃ ) / ³⁶C₅ ​​​​​​​

= 0.01641414 + 0.1199495 + 0.3084416

= 0.4448052

The correct answer is a) 0.4448

4.

Probability that it will be shipped = Probability that there is no defective toys selected out of 9 toys in which 2 are defective and 7 are not defective

= ( ⁷C₃ * ²C₀ ) / ⁹C₃

= 0.4166667

The correct answer is e) 0.4167