A darts player throws two darts, attempting to score a bull's-eye with each. The probability that he will achieve this with his first dart is 0.25 . If he misses with his first dart, the probability that he will also miss with his second dart is 0.7 . The probability that he will miss with at least one dart is 0.9 .
Show that the probability that he succeeds with his first dart but misses with his second is 0.15 .
Find the conditional probability that he misses with both darts, given that he misses with at least one.
The entrance to a car park is 1.9 m wide. It is found that this is too narrow for \(2 \%\) of the vehicles which need to use the car park. The widths of these vehicles are modelled by a normal distribution with mean 1.6 m .
Find the standard deviation of the distribution.
It is decided to widen the entrance so that \(99.5 \%\) of vehicles will be able to use it.