SOLUTION: the probabaility that a car will have a flat tire while driving through a tunnel is 0.006. Find the probability that 2 of 5000 cars passing through the tunnel will have flat tires.

Question 1100985: the probabaility that a car will have a flat tire while driving through a tunnel is 0.006. Find the probability that 2 of 5000 cars passing through the tunnel will have flat tires.
please help me with this.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
this is a binomial probability type problem.

the formula to use is p(x) = c(n,x) * p^x * q^(n-x)

n is the total number of possible occurrences.
p is the probability that one occurrence happens.
q is the probability that one occurrence doesn't happen.
q is equal to 1 - p.
p^x is the probability of x occurrences happening.
q^(n-x) is the probability of (n-x) occurrences not happening.
c(n,x) is the number of ways you can get x occurrences out of n possible occurrences where order is not important.

in your problem:
n is 5000.
x is equal to 2
n-x is equal to 5000 - 2 which is equal to 4998
p is equal to .006
q is equal to 1 - .006 = .994
c(5000,2) is equal to 12497500

the formula of p(x) = c(n,x) * p^x * q^(n-x) becomes:

p(2) = c(5000,2) * .006^2 * .994^4998

c(5000,2) = 5000! / (2! * 4998!)
this is the same as c(5000,2) = (5000 * 4999 * 4998!) / (2! * 4998!)
the 4998! in the numerator and denominator cancel out and you are left with:
c(5000,2) = (5000 * 4999) / 2!
since 2! is equal to 2, then your answer becomes:
c(5000,2) = (5000 * 4999) / 2 and the result is:
c(5000,2) = 12497500.

the formula of p(2) = c(5000,2) * .006^2 * .994^4998 becomes:
p(2) = 12497500 * .006^2 *.994^4998 which results in:
p(2) = 3.89291449 * 10^-11.

that's a very small probability.

in decimal notation, p(2) = .0000000000389291449

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