# In a survey, 510 adults were asked if they drive a pickup truck and if they drive a Ford.  The results showed that 1 in 6 adults surveyed drives a pickup truck, and 3 in 10 adults drive a Ford. Of the adults surveyed that drive a Ford, 2 in 9 drive a pickup truck.  Find the probability that a randomly selected adult drives a Ford and drives a pickup truck.

Question

In a survey, 510 adults were asked if they drive a pickup truck and if they drive a Ford.  The results showed that 1 in 6 adults surveyed drives a pickup truck, and 3 in 10 adults drive a Ford. Of the adults surveyed that drive a Ford, 2 in 9 drive a pickup truck.  Find the probability that a randomly selected adult drives a Ford and drives a pickup truck.

Step 1

Given information:

From the survey in which 510 adults were asked about the status of driving a pickup truck and ford, the following things can be noted:

Denote the event “a randomly selected adult drives a pickup truck” as A.

It is given that 1 in 6 adults surveyed drives a pickup truck.

The probability that a randomly selected adult drives a pickup truck is P(A) = (1/6).

Denote the event “a randomly selected adult drives a Ford” as B.

It is given that 3 in 10 adults surveyed drive a Ford.

The probability that a randomly selected adult drives a Ford is P(B) = (3/10).

The event “a randomly selected adult drives a pickup truck given that he drives a Ford” is A/B.

It is given that 2 in 9 adults surveyed drive a pickup truck given that they drive a Ford.

The probability that a randomly selected adult drives a pickup truck given that he drives a Ford is P(A/B) = (2/9).

Step 2

Find the probability that a randomly selected adult drives a Ford and a pickup truck:

The probability that a randomly selected adul...

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