In Problems 2732 a fair coin is tossed 8 times 27 What is th

In Problems 27-32, a fair coin is tossed 8 times. 27. What is the probability of obtaining exactly 1 hea 28. What is the probability of obtaining exactly 2 29. What is the probability of obtaining at least 5 tails? 30. What is the probability of obtaining at most 2 tails? 31. What is the probability of obtaining exactly 2 heads if it ng exactly I head? ds? hea is known that at least 1 head appeared? 32. What is the probability of obtaining exactly 3 heads if it is known that at least 1 head appeared? Applications 37 Quality Control Suppose that 5% of the items produced by a factory are defective. If 8 items are chosen at random, what is the probability (a) Exactly 1 is defective? (b) Exactly 2 are defective? (c) At least 1 is defective? (d) Fewer than 3 are defective? 38, Opinion Poll Suppose that 60% of the voters intend to vote for a conservative candidate. What is the probability a survey polling 8 people reveals that 3 or fewer intend to vote for a conservative candidate? 39. Family Structure What is the probability in a family with exactly 6 children (a) 3 are boys? (b) At least 5 are boys? (c) At least 2, but less than 4, are girls? 40. Family Structure What is the probability in a family of 7 children: (a) 4 are girls?

Solution

Total number of outcomes = 2^8 = 256

27)

Cases of only one head = 8C1 = 8! / (1! * 7!) = 8

P(One head ) = 8/256 = 0.03125 Answer

28)

Cases of two head = 8C2 = 8! / (2! * 6!) = 28

P(two head) = 28/256 = 0.1094 Answer

29)

Cases of atleast five tails = 8C5 + 8C6 + 8C7 + 8C8

= 8! / (3! * 5!) + 8! / (2! * 6!) + 8! / (1! * 7!) + 8! / (0! * 8!) =93

P( atleast five tails ) = 93/256 = 0.3633 Answer

30)

Cases of atmost two tails = 8C0 + 8C1 + 8C2

= 8! / (2! * 6!) + 8! / (1! * 7!) + 8! / (0! * 8!) =37

P( atmost two tails) = 37/256 = 0.1445 Answer

As per chegg Q&A guidelines I have answered first four subparts of this problem.