Question

Do you know Squidward? According to a survey by Nickelodeon TV, 82% of children under 13 in Germany recognized a picture of the cartoon character SpongeBob SquarePants. Assume that among those children, 83% also recognized SpongeBob's cranky neighbor Squidward Tentacles. What is the probability that a German child recognized both SpongeBob and Squidward? Write your answer as a fraction or a decimal, rounded to four decimal places.

Answer 1

To find the probability that a German child recognized both SpongeBob and Squidward, we can use the formula:

P(A and B) = P(A) * P(B | A)

where A and B are events, P(A) is the probability of event A, and P(B | A) is the probability of event B given that event A has occurred.

Let A be the event that a child recognized SpongeBob, and let B be the event that a child recognized Squidward. Then:

P(A) = 0.82 (given)
P(B | A) = 0.83 (given)

So the probability that a German child recognized both SpongeBob and Squidward is:

P(A and B) = P(A) * P(B | A) = 0.82 * 0.83 = 0.6806

Rounding to four decimal places, the probability is 0.6806, or approximately 0.681 as a decimal or 681/1000 as a fraction. Therefore, the probability that a German child recognized both SpongeBob and Squidward is about 0.681.