Question

A trainer is teaching a dolphin to do a trickThe probability that the dolphin successfully performs the trick is 37, and the probability that the dolphin does not successfully perform the trick is 63%Out of 5 attempts, what is the probability that the dolphin successfully performs the trick at most 2 times? Round your answer to three decimal places. Do not enter the probability in terms of percentage

Answer 1

To find the probability that the dolphin successfully performs the trick at most 2 times out of 5 attempts, we need to calculate the probabilities of the dolphin performing the trick 0 times, 1 time, and 2 times and add these probabilities together.

Step-by-step explanation:

To find the probability that the dolphin successfully performs the trick at most 2 times out of 5 attempts, we need to consider the different possibilities.

The probability of the dolphin successfully performing the trick is 37%, and the probability of not successfully performing the trick is 63%. In order to calculate the probability of the dolphin performing the trick at most 2 times, we need to calculate the probability of the dolphin performing the trick 0 times, 1 time, and 2 times, and add these probabilities together.

The probability of the dolphin performing the trick 0 times is (0.63)^5 = 0.077.

The probability of the dolphin performing the trick 1 time is 5 * (0.37)*(0.63)^4 = 0.205.

The probability of the dolphin performing the trick 2 times is (5 choose 2) * (0.37)^2 * (0.63)^3 = 0.369.

Adding these probabilities, we get 0.077 + 0.205 + 0.369 = 0.651.