Three highwatys connect city A with City B Two highways conn

Three highwatys connect city A with City B. Two highways connect city B with city C. During a rush hour, each highway is blocked by a traffic accident with the probability 0.2, independently of other highways.

A) Compute the probability that there is at least one open route from A to C.

B) How will a new highway, also blocked with probability 0.2 independently of other highways, change the probability in (a) if it is built.

***Please explain to whoever answers***

Solution

answer a) As there are 3 highway A to B and 2 from B to C so there are 6 different routes from A to C each consisting of 2 highways

As each highway is blocked with probability 0.2 so a route will be blocked with probability 0.04 so total there are 6 routes so probability all will be blocked is 6* 0.04 = 0.24

So probalibilty alteast one will not be blocked = 1- 0.24 = 0.76

Ans B) As probability of the all the highways beign blocked is 0.2 independent of other highways so probability in A will decrease as no. of routes will increase