Question

A recent survey of people who eat salad suggest that 78% like tomatoes on their salad, 49% like cheese on their salad, and 36% like both tomatoes and cheese on their salad. suppose a person who eats salad is selected at random, and find they like cheese on their salad. what is the probability that the person also likes tomatoes on their salad? 0.29 0.46 0.49 0.73

Answer 1

By definition of conditional probability, the probability that the person also likes tomatoes on their salad is 0.73 or 73% (last option).

Definition of probability

Probability is the greater or lesser possibility that a certain event will occur.

In other words, the probability establishes a relationship between the number of favorable events and the total number of possible events.

Definition of conditional probability

The conditional probability P(A|B) is the probability that an event A occurs, knowing that another event B also occurs. That is, it is the probability that event A occurs if event B has occurred. Is defined as:

P(A|B) = P(A∩B)÷ P(B)

Probability that the person also likes tomatoes on their salad

In this case, you know:

• Event A: Person likes tomatoes on their salad.
• Event B: Person likes cheese on their salad.

Being the event A∩B (A intersection B) when A and B occur simultaneously, then:

• P(A)= 78%=0.78
• P(B)= 49%= 0.49
• P(A∩B)= 36%=0.36

Suppose a person who eats salad is randomly selected and likes cheese on his salad, the probability that the person also likes tomatoes on their salad is:

P(B|A) = P(A∩B)÷ P(B)

Then:

P(A|B) = 0.36÷0.49

P(B|A) = 0.73= 73%

Finally, the probability that the person also likes tomatoes on their salad is 0.73 or 73% (last option).

Learn more about conditional probability:

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