In problem 5 we discuss tossing a coin three times. Each toss can have one of two outcomes. Letting 0 = tails and 1 = heads we have the sample space in Table 1 below. The event the exactly one toss results in a head is {001 010 100}, P(E) = 3/8 = .375. The event that at least two tosses result in a head is {011 101 110 111}, P(E) = 4/8 = .5. The event that no head is obtained is {000}, P(E) = 1/8 = .125.
In problem 6 we discuss a family with three children. Each child is either a boy (0) or a girl (1). We have the sample space in Table 1 below. The event the exactly one child is a girl is {001 010 100}, P(E) = 3/8 = .375. The event that at least two children are girls is {011 101 110 111}, P(E) = 4/8 = .5. The event that no child is a girl is {000}, P(E) = 1/8 = .125.
In problem 7 we discuss a true(1)/false(0) exam with three questions. The probability that exactly one is correct with random guessing is .375, that at least one is correct is .5, and that no answer is correct is .125 or 12.5%.
In problem 8 we discuss exposure to illness with a 50-50 chance of catching the illness. The results are the same, only the names have changed.
Table 1
000
001
010
011
100
101
110
111