Question

A 13 card hand is dealt from a well-shuffled standard 52-card deck. What is the probability that 6 red cards and 7 black cards are dealt?

a) 0.2785

b) 0.2385

c) 0.2885

d) 0.2355

e) 0.2985

f) None of the above.

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Question 2

An urn contains 13 red marbles and 14 blue marbles. 16 marbles are chosen at random. What is the probability that 6 red marbles are chosen?

a) 0.000006

b) 0.131748

c) 0.000614

d) 0.000208

e) 0.000132

f) None of the above.

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Question 3

An urn contains 11 white balls and 8 green balls. A sample of seven is selected at random. What is the probability that the sample contains at least one green ball?

a) 0.9998

b) 0.9935

c) 0.9266

d) 0.0734

e) 0.0002

f) None of the above.

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Question 4

A fair coin is tossed 14 times. What is the probability that the coin lands head at least 12 times?

a) 0.0056

b) 0.0063

c) 0.0129

d) 0.0065

e) 0.0064

f) None of the above.

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Question 5

A fair coin is tossed 25 times. What is the probability that at most 22 heads occur?

a) 0.999922

b) 0.000078

c) 0.999990

d) 0.000069

e) 0.000010

f) None of the above.

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Question 6

A fair coin is tossed 25 times. What is the probability that at least 3 tails occur?

a) 0.000068545

b) 0.999921739

c) 0.999990284

d) 0.000000030

e) 0.999990314

f) None of the above.

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Question 7

A business organization needs to make up a 5 member fund-raising committee. The organization has 10 accounting majors and 8 finance majors. What is the probability that at most 1 accounting major is on the committee?

a) 0.0012

b) 0.0817

c) 0.0065

d) 0.0882

e) 0.0077

f) None of the above.

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Question 8

A classroom of children has 13 boys and 17 girls in which five students are chosen at random to do presentations. What is the probability that more boys than girls are chosen?

a) 0.2820

b) 0.0090

c) 0.3582

d) 0.3673

e) 0.0853

f) None of the above.

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Question 9

A toy manufacturer inspects boxes of toys before shipment. Each box contains 8 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) 0.4667

b) 0.1071

c) 0.3571

d) 0.6429

e) 0.9231

f) None of the above.

Answer 1

SOLUTION:

From given data,

Question 1

A 13 card hand is dealt from a well-shuffled standard 52-card deck. What is the probability that 6 red cards and 7 black cards are dealt?

In 52 cards choose = 13

ⁿC_r = n! /[ r! *(n-r)!]

⁵²C₁₃ = 25! / [ 13! *(52-13)!]

= 25! / (13! * 39!)

= 635013559

Select 6 cards from 26 : ²⁶C₆ = 26! / [ 6! *(26-6)!]

= 26! / [ 6! *(20)!]

=  230230

Select 7 cards from 26 : ²⁶C₇ =  26! / [ 7! *(26-7)!]

   = 26! / [ 7! *(19)!]

= 657800

so required probability : ( ²⁶C₆ + ²⁶C₇ ) /  ⁵²C₁₃

= (230230*657800) /  635013559600

= 0.2385

Answer : option b) 0.2385

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