The probability that an individual commutes to work by car is 0.9. Wha

kiki195ms

kiki195ms

Answered question

2021-11-13

The probability that an individual commutes to work by car is 0.9. What is the probability that ten neighbors all commute by car? What is the probability that none of them commute by car?

Answer & Explanation

Witionsion

Witionsion

Beginner2021-11-14Added 19 answers

Step 1
Given data:
The given probability that individual commutes to work by car is p=0.9.
The total numbers of neighbors are n=10.
Write the expression for the probability that all neighbors commute by car.
P(10)=nC10(p)10(1p)1010
=nC10(p)10
Substitute the given values in the above expression.
P(10)=10C10(0.9)10
=10!0!(10!)(0.9)10
=0.3487
Thus, the probability that all neighbors commute by car is 0.3487.
Step 2
Write the expression for the probability that none of the neighbors commute by car.
P(0)=nC0(p)0(1p)100
=nC0(1p)10
Substitute the given values in the above expression.
P(0)=10C0(10.9)10
=10!10!(0!)(0.1)10
=0.110
Thus, the probability that none of the neighbors commute by car is 0.110.

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