Week 5 Worksheet 9 MATH 10B
Tu 2/21/19
1. A weather forecaster in Brooklyn reports the following: The probability it will snow
today is .7. The probability it will snow tomorrow is .5. The probability it will snow
today and tomorrow is .3. The probability it will snow today or tomorrow is .9.
Define an appropriate sample space, write these expressions in terms of unions and
intersections of subsets of the sample space, and assess if this is a reasonable statement
to make.
Solution: The sample space is the four possibilities of snow; it snows today and
tomorrow, it snows today but not tomorrow, it snows tomorrow but not today, or
it snows neither day. Call Athe event that it snows today, and Bthe event that
it snows tomorrow. These can be expressed as
P(A) = .7, P (B) = .5, P (A∩B) = .3, P (A∪B) = .9
We need P(A∪B) = P(A)+ P(B)−P(A∩B) for this statement to be reasonable.
Here this is the case.
2. original A family has three children. Assume that the probability of each child being
a boy or girl is 50% each.
(a) What is the probability the family has exactly two girls if there is at least one
girl?
Solution: Using conditional probability, the probability of there being at
least one girl (A) is 1 −1
23=7
8. The probability of there being exactly two
girls Bis 3
21
23=3
8.B⊂A, so
P(B|A) = P(A∩B)
P(A)=P(B)
P(A)=3
7
(b) What is the probability the family has exactly two girls if the oldest child is a
girl?
Solution: P(B|A) is now the probability that exactly one of the next two
children is a girl, or 2
11
4=1
2
3. 7.2.29 A group of 6 people are playing a game of “odd person out” to determine who
will buy refreshments. Each person flips a fair coin. If there is a person whose outcome
is not the same as that of any other member of the group, this person has to buy the
refreshments. What is the probability that there is an odd person out after the coins
are flipped once?
1
