Question

The average travel time to a distant city is c hours by car or b hours by bus. A woman cannot decide whether to take the bus or drive , so she tosses a coin, what is her expected travel time?

Answer 1

Answer:

The expected travel time 'b + c'

Step-by-step explanation:

Given,

The time taken by bus = b hours,

Time taken by car = c hours,

If she decide the journey by coin,

Case 1 : Let she travels in bus if she gets head,

∵ Probability of getting head = $\frac{1}{2}$

Probability of getting tail = $\frac{1}{2}$

So, the expected travel time = $\frac{1}{2}\times b+\frac{1}{2}\times c$

$=\frac{b}{2}+\frac{c}{2}$

Case 2 :Let she travels in bus if she get tail,

So, the expected travel time = $\frac{1}{2}\times b+\frac{1}{2}\times c$

$=\frac{b}{2}+\frac{c}{2}$

Hence, the expected travel time = $\frac{b}{2}+\frac{c}{2}+\frac{b}{2}+\frac{c}{2}$

= b + c