Question

A trainer is teaching a dolphin to do tricks. The probability that the dolphin successfully performs the trick is 35%, and the probability that the dolphin does not successfully perform the trick is 65%. Out of 20 attempts, you want to find the probability that the dolphin succeeds 12 times. State the probability question mathematically.

Short answer

The probability question is stated mathematically as to find$P(X=12)$

Step-by-step solution

Content Introduction

We are given the information:

The probability that the dolphin successfully performs the trick is $35\%$

the probability that the dolphin does not successfully perform the trick is$65\%$

Content Explanation

Here the random variable

$$\begin{gathered} X=numberofsuccessfulperformancesoftricksbydolphinoutof20attempts. \\ Xassumesthevalues0,1,2,3,........,20 \end{gathered}$$

The probability that the dolphin successfully performs the trick is role="math" localid="1648148479492" $p=35\%$

the probability that the dolphin does not successfully perform the trick is $q=65\%=0.65$

The number of attempts by dolphin is $n=20$

Therefore, The probability question is stated mathematically as to find$P(X=12)$