Problem $1$: The route used by a certain motorist in commuting to work contains two highways.

The probability that the first highway is congested is $0\mathrm{.}4.$ The probability that the second highway

is congested is $0\mathrm{.}5.$ If the first highway is congested then the probability that the second highway

is congested is $0\mathrm{.}6.$ Determine the probability that

the first highway is not congested? $(1$ point$)$

both highways are congested? $(1$ point$)$

atleast one of the highways is congested? $(2$ points$)$

the first highway is congested but not the second highway? $[$Hint: The event which is being

asked is similar to the last part of the last example in Lecture $2.$ Write down the event and

then draw the Venn diagram to identify, how the probability can be calculated using the

information you have now.$](2$ points$)$