Chapter 8.6, Problem 25E

To determine

To find: the probability of winning a lottery that aplayer who buys one ticket matches all n numbers drawn (in any order ).

Answer to Problem 25E

Probability of winning is $P(E)=\frac{1}{8,436}.$

Explanation of Solution

Given information: A player chooses n numbers from a to b in a lottery. Where n =3,

a =0, b =37.

Formula used:

If an event has n(E) equally likely outcomes and its sample space S has n(S) equally likely outcomes, then the probability of event is given by,

  $P(E)=\frac{n(E)}{n(S)}.$

Formula for the number of combinations of n numbers taken r numbers at a time is,

  $n(S){=}_n{C}_r.$

Calculation:

To find the outcomes in the sample space, use the formula for the number of combination of 38 (0 to 37) numbers taken 3 numbers at a time.

  $n(S){=}_n{C}_r{=}_{38}{C}_3=\frac{38\times 37\times 36}{3\times 2\times 1}=8,436.$

Player buys one ticket, n ( E) =1 ,the probability of winning is,

  $P(E)=\frac{n(E)}{n(S)}=\frac{1}{8,436}.$