Browsing as Guest. Progress, bookmarks and attempts are disabled.
Log in to track your work.
Nov 2015 p63 q7
3074
A factory makes water pistols, 8% of which do not work properly.
In a random sample of n water pistols, the probability that at least one does not work properly is greater than 0.9. Find the smallest possible value of n.
Solution
The probability that a water pistol works properly is 92% or 0.92.
The probability that all n water pistols work properly is given by:
\(P(0) = (0.92)^n\)
We want the probability that at least one does not work properly to be greater than 0.9:
\(1 - P(0) > 0.9\)
Substituting for \(P(0)\):
\(1 - (0.92)^n > 0.9\)
Rearranging gives:
\((0.92)^n < 0.1\)
Taking logarithms on both sides:
\(n \log(0.92) < \log(0.1)\)
Solving for \(n\):
\(n > \frac{\log(0.1)}{\log(0.92)}\)
Calculating gives:
\(n > 27.6\)
Since \(n\) must be an integer, the smallest possible value is: