Winston, a dog, loves to play fetch.  He catches each ball mid-air independently with probability 0.4.  What is the probability that in four tosses, Winston makes exactly three mid-air catches? Round your answer to three decimal places.

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Winston, a dog, loves to play fetch.  He catches each ball mid-air independently with probability 0.4.  What is the probability that in four tosses, Winston makes exactly three mid-air catches? Round your answer to three decimal places. 

Expert Solution
Step 1

Obtain the probability that in four tosses, Winston makes exactly three mid-air catches.

 

The probability that in four tosses, Winston makes exactly three mid-air catches is obtained below as follows:

 

From the information, given that

 

Let X denotes the number of mid-air caches which follows binomial distribution with the probability of success 0.40 with the random sample of 4 tosses has been made.

 

That is, n=4, p=0.4.

 

The probability distribution is given by,

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