Question

Ou randomly choose one of the tiles. Without replacing the first tile, you choose a second tile. What is the probability of the compound event? Write your answer as a fraction or percent rounded to the nearest tenth.

Answer 1

1/42

Explanation:

In this problem, we have 7 tiles in total, which are numbered: 5, 6, 7, 8, 9, 10, 20.

We need to find the probabilty of getting 5 first, and 6 second.

First of all, notice that these events are independent, because choosing one number doesn't increase or decrease the probability of chossing another one. Therefore, we solve this problem multiplying probabilities, that's the compound event. Also, after the first pick, the total number of outcomes decreases, because tiles aren't being replace after picked.

Probability of 5.

`P_(5) =(1)/(7)`

Becasue, there's only one tile numbered 5.

Probability of 6.

`P_(6) =(1)/(6)`

Because there's only one tile numbered 6, and the first tile picked is not being replaced.

Now, the compound event probability is

`P=(1)/(7) * (1)/(6)=(1)/(42)`

Therefore, the answer is 1/42.