Question

If the odds of winning the prize is 1 : 53 and If I purchased 84 tickets what are the odds of winning in percentage. Step by step?

Answer 1

79.81% probability of winning.

Explanation:

For each ticket, there are only two possible outcomes. Either you win, or you do not. The probability of winning in a ticket is independent of other tickets. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

In which
`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

And p is the probability of X happening.

The odds of winning the prize is 1 : 53

This means that
`p = (1)/(53)`

If I purchased 84 tickets what are the odds of winning in percentage.

To win, at least one of the tickets must have the prize, of 84 tickets, so
`n = 84`.

We have to find
`P(X \geq 0)`, which is given by:

`P(X \geq 0) = 1 - P(X = 0)`

In which

`P(X = 0) = C_(84,0).((1)/(53))^(0).((52)/(53))^(84) = 0.2019`

`P(X \geq 0) = 1 - P(X = 0) = 1 - 0.2019 = 0.7981`

79.81% probability of winning.