the probability of a house will be burglarized is = 5% which is = .05
the probability of a house will NOT be burglarized is = (1 - .05)
the probability of a second house will NOT be burglarized is =
(1-.05)*(1-.05)= (1-.05)^2
the probability of a third house will NOT be burglarized is=
(1-.05)*(1-.05)(1-.05)= (1-.05)^3
so, the probability of NONE = (1-.05)^10 = .598736939 = .5987
The probability that both will be hopelessly romantic is .0081 .009^2 = .0081
Empirical
50%
50 percent
The probability is approx 0.81
Only one selected 68%
It is 0.73 = 0.343
Using the Poisson approximation, the probability is 0.0418
The probability that both will be hopelessly romantic is .0081 .009^2 = .0081
The probability is 10 percent.
The probability that exactly 4 out of 6 randomly selected vehicles will pass the test when the pass rate is 80% is approx 0.2458 (or nearly a quarter).
1 - (3/10 x 3/10 x 3/10) ie 1 - 27/1000 ie 0.973
Empirical
50%
50 percent
The probability is approx 0.81
Empirical