The probability of a player scoring a goal is 0.70. what is the probab

varaderiyw

varaderiyw

Answered question

2021-11-15

The probability of a player scoring a goal is 0.70. what is the probability that a the 5th goal is made on the players 8th shot? what is the expected value of the probability?

Answer & Explanation

Robert Harris

Robert Harris

Beginner2021-11-16Added 23 answers

Step 1
The probability of a player scoring a goal is 0.70
The probability that a 5th goal is made on the 8th shot is to be calculated. This is a probelm of negative binomial experiment. The probability of a success is 0.70. The number of trials =8. The number of successes is 5. To solve this, we are using negative binomial formulas i.e,
NB(x,r,p)=x1cr1pr(1p)xr
Here, r=5,x=8,p=0.7
NB(8,5,0.7)=7c40.75(1p)xr
=7c40.750.33
=0.1588
The answer is 0.1588
Step 2
Now, the expected value of probability is obtained by using the following formula:
Let μ denote the expected value then,
μ=rp
where,
r= number of success =5
p= probability of success =0.7
μ=50.7
=7.1428
The expected value of the probability is 7.1428

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