An insurance company reported that 75​% of all automobile da

Ashley Bell

Ashley Bell

Answered question

2021-12-19

An insurance company reported that 75​% of all automobile damage claims were made by people under the age of 25.
If ten automobile damage claims were selected at​ random, determine the probability that exactly two of them were made by someone under the age of 25.
The probability is ?.
​(Type an integer or decimal rounded to five decimal places as​ needed.)

Answer & Explanation

Raymond Foley

Raymond Foley

Beginner2021-12-20Added 39 answers

Step 1
Introduction:
Total number of observations, n=10.
Let X= number of automobile damage claims out of 10, that were made by people under 25 years of age.
Probability of “success” (success- a claim is by someone who is below 25 years) is, p=0.75.
X~Binomial10,0.75.
Step 2
Calculation:
The probability that exactly two out of 10 claims were made by someone under the age of 25 is,
PX=2
=nCxpx1-pn-x
=10C20.7521-0.7510-2
=0.000386
0.00039.
Thus, the required probability is 0.00039.

Archie Jones

Archie Jones

Beginner2021-12-21Added 34 answers

This would be 8C5(0.6)5(0.4)3=560.07760.064
without rounding, calculate
=0.2787
nick1337

nick1337

Expert2021-12-28Added 777 answers

The probability p that any individual avtomob. damage claim was made by a person under age 25 is 75%.
means p=0.75=success
Now probability q than damage claim was not made by a person under the age of 25,
q=1p
q=10.75
q=0.25
for finding the desired no of success x over n trials, we use binomial probability distribution
P(n)=ncxpxqnx{n=7 n=2}
11=7c2(0.75)2(0.25)72
11=7!(72)!2!×0.0005493164
11=7×6×5!5!×2×1×0.0005493164
P(x)=0.011536

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