Question

The Sorry State Lottery requires you to select five different numbers from 0 through 42. (Order is not important.) You are a Big Winner if the five numbers you select agree with those in the drawing, and you are a Small-Fry Winner if four of your five numbers agree with those in the drawing. (Enter your answers as exact answers.) What is the probability of being a Big Winner?

Answer 1

1 / 962598

Explanation:

Let S be the sample space

total number of possible outcomes = n(S)

Let E be the event

total number of favorable outcomes = n(E)

Compute the number of ways to select 5 numbers from 0 through 42:

Total numbers to choose from = 43

So

Total number of ways to select 5 numbers from 43

= n(S) = 43C5

= 43! / 5! ( 43-5)!

= 43! / 5! 38!

= 43*42*41*40*39*38! / (5*4*3*2*1)*38!

= 115511760/120

n(S) = 962598

Hence there are 962598 ways to select 5 numbers from 43

Compute the probability of being a Big Winner

In order to be a Big Winner all 5 of the 5 winning balls are to be chosen and there is only one way you can for this event to occur. So

n(E) = 1

Here E is to be a Big Winner

So probability of being a Big Winner = P(E)

= n(E) / n(S)

= 1 / 962598

Hence

P(being a Big Winner) = P(E) = 1 / 962598