Question

Holiday meals from different traditions include seafood, ham, beef, vegetarian, turkey, or other fowl and various side dishes. A survey of US families revealed that 58% of all families eat turkey at holiday meals ("T"), 42% eat vegetarian dishes ("V"), and 19% have both turkey and vegetarian dishes to eat at holiday meals. A family is selected at random. (Drawing shaded Venn diagrams may help determine the probabilities in the questions.)

a) What is the probability that the selected family had vegetarian dishes or a turkey?

b)What is the probability that the selected family had neither vegetarian dishes nor turkey?

c)What is the probability that the selected family had turkey but no vegetarian dishes?

d)"Families having turkey are disjoint from the families having vegetarian dishes." This statement is:

-True because P(T and V) ? -P(T)×P(V)
- False because P(T and V) ? P(T)×P(V)
-True because P(T and V) ? 0
-False because P(T and V) ? 0

Answer 1

Solution:

Venn Diagram is given below:

a) What is the probability that the selected family had vegetarian dishes or a turkey?

Answer: The probability that the selected family had vegetarian dishes or a turkey is given below:

P(turkey or vegetarian)

  

  

Therefore, the probability that the selected family had vegetarian dishes or a turkey is

b)What is the probability that the selected family had neither vegetarian dishes nor turkey?

Answer: The probability that the selected family had neither vegetarian dishes nor turkey is given below:

P(neither turkey nor vegetarian) = 1 - P(turkey or vegetarian)

  

  

Therefore, the probability that the selected family had neither vegetarian dishes nor turkey is

c)What is the probability that the selected family had turkey but no vegetarian dishes?

Answer: The probability that the selected family had turkey but no vegetarian dishes is given below:

P(turkey only) = P(turkey) - P(turkey and vegetarian)

Therefore, the probability that the selected family had turkey but no vegetarian dishes is

d)"Families having turkey are disjoint from the families having vegetarian dishes." This statement is:

Answer: False,

The events are not disjoint, since some families (19%) have both turkey and vegetarian dishes at their holiday meals.