Question

There are 100 prize tickets in a bowl, numbered 1 to 100. What is the probability

that an even numbered prize ticket will be chosen at random, not replaced, then an
odd numbered prize ticket will be chosen? Does this represent an independent or
dependent event? Explain.

Answer 1

25/99

Dependent event

Explanation:

1. Multiply the possibilities

There are 50 even numbers out of 100 numbers. If one even number is drawn and not replaced, that would leave the odd ticket to be drawn out of 99 tickets. Because an even number was drawn first, all 50 odd numbers would remain.

`(50)/(100)` ·
`(50)/(99)` =
`(2500)/(9900)`

Simplify

`(2500)/(9900)` =
`(25)/(99)`

2. This is a dependent event because the chances of an odd number being drawn was altered. If the even ticket was replaced, the probability of the odd number being drawn would not have been affected.

Answer 2

25/99; Dependent event

Explanation:

This is the probability that an even ticket will be chosen out of 100 tickets times the probability that an odd ticket will be chosen out of the remaining 99 tickets.

There 50 even out of 100 to start off with. After 1 even is chosen there are still 50 odd but only 99 more tickets.

(50/100)(50/99)=2500/9900= 25/99

This is a dependent event because an odd number should come after the even number only.