APPLICATIONS

Slot Machine A slot machine has three wheels. Each wheel has 11 positions: a bar and the digits 0 , 1 , 2 ,…, 9 . When the handle is pulled, the three wheels spin independently before coming to rest. Find the probability that the wheels stop on the following positions.

(a) Three bars

(b) The same number on each wheel

(c) At least one bar

(a)

To find:

The probability that the wheels will stop on three bars.

Given:

The slot machine has three wheels and each wheel has 11 positions: a bar and digits 0,1,2,...,9. The wheels spin independently.

Approach:

Let S be the sample space and all outcomes are equally likely. The probability of an event E denoted by P(E) is,

P(E)=n(E)n(S)=number of favourable outcomestotal number of outcomes …(1)

The probability of intersection of independent events E and F is,

P(E∩F)=P(E)P(F) …(2)

Calculation:

Let E be the event when the first wheel stops on a bar, F be the event that the second wheel stops on the bar, and H the third wheels stops on the bar

(b)

To find:

The probability that the wheels stop on the same number on each wheel.

(c)

To find:

The probability that the wheels stop on at least one bar.