Question

Passengers try repeatedly to get a seat reservaton in any train running between two stations until they are successful. If there is 40% chance of getting reservation in any attempt by a passenger then the average number of attempts that passengers need to make to get a seat reserved is

• A. 3

Answer 1

The correct option is A 3

Probability of getting reservation = 40%

Hence, if he books 2.5 ticket he will get a confirmed ticket.

So, atleast 3 ticket to be booked to get a confirmed reservation.

Method II:

where P(W) = 0.4, P(L) = 0.6 & X = {No. of attempts}

So Probability Distribution is

$(\begin{array}{cccccc}X:& 1& 2& 3& 4& ....\\ P\left(X\right):& 0.4& (0.6)0.4& {(0.6)}^{2}0.4& {(0.6)}^3(0.4)& .....\end{array}$

So $E\left(X\right)=\sum p_i{x}_i$

$=1\times 0.4+2\times \left(0.6\right)\left(0.4\right)+3\times \left(0.6{)}^2\right(0.4)+4\times (0.6{)}^3\times \left(0.4\right)+.....$

$=0.4[1+2x+3x^2+4x^3+.....]$

where x = 0.6

$=\left(0.4\right)(1-x{)}^{-2}=2.5$

So passenger needs to book atleast 3 tickets.