Question

Timmy has two boxes of toys. The first box contains 3 trucks and 7 cars; the second box contains 6 trucks and 3 cars. On Monday, Timmy selected one of the toys at random from the first box and placed it in the second box. The next day, Tuesday, he selected a toy at random from the second box. Given that the toy he selected on Tuesday was a car, what is the probability that the toy he selected on Monday was also a car?

Answer 1

To find the probability that the toy Timmy selected on Monday was also a car, given that the toy he selected on Tuesday was a car, we can use conditional probability. The probability is approximately 1.925.

Step-by-step explanation:

To find the probability that the toy Timmy selected on Monday was also a car, given that the toy he selected on Tuesday was a car, we can use conditional probability.

Let's define the events:

• A: The toy Timmy selected on Monday was a car.
• B: The toy Timmy selected on Tuesday was a car.

We want to find P(A|B), the probability that A occurs given that B occurs. According to the problem, there are 7 cars and 10 toys in the first box, and after Timmy moves one toy to the second box, there are 11 toys in the second box, including 4 cars.

Using conditional probability formula:

P(A|B) = P(A ∩ B) / P(B)

P(A ∩ B) is the probability that Timmy selected a car on both Monday and Tuesday. Since Timmy selected a car on Tuesday, there are 4 cars in the second box, and the probability of selecting a car on Monday was 7/10.

P(B) is the probability that Timmy selected a car on Tuesday. Since there are 11 toys in the second box, and 4 of them are cars, the probability is 4/11.

Substituting the values into the formula, we have:

P(A|B) = (7/10) / (4/11)

Simplifying, we get:

P(A|B) = (7/10) * (11/4) = 77/40 = 1.925

Therefore, the probability that the toy Timmy selected on Monday was also a car, given that the toy he selected on Tuesday was a car, is approximately 1.925.