Question

You randomly choose a tile. Without replacing the first tile, you choose a second tile. Find the probability of the compound event. Write your answer as a fraction or percent rounded to the nearest tenth. The probability of choosing a number less than 7 and then a multiple of 4 is?

Answer 1

`(2)/(21)` or 9.5%

Explanation:

The probability of any event can be represented by a fraction where the denominator is the number of total outcomes and the numerator is the number of desired outcomes. In this problem, the events are dependent, meaning that the results of the events are affected by previous events. Since there are only 7 total tiles, if you do not replace the first one, you have only 6 tiles left for the second choice.

First choice: Probability of a number less than 7: 5 or 6, so 2 out of 7:
`(2)/(7)`

Second choice: Probability of a multiple of 4: 8 or 20, so 2 out of 6 (since one was taken and not replaced):
`(2)/(6)`

Combined probability:
`(2)/(7)*(2)/(6)=(4)/(42)=(2)/(21)` or 9.5%