Question

Pamela has a sack that contains the letter tiles shown here. D T A O E A H E E D U O A H T. Without replacement, Pamela will randomly select 2 tiles fron the sack one at a time. What is the probability that she will select the letter E first and the letter T second?

Answer 1

We have 15 letter tiles. Out of those 15 tiles, we have 3 E and 2 T.

Thereby, the probability of picking an E first is:

`(3)/(15)\rightarrow(1)/(5)`

Since Pamela does not replace the tiles, we would now have 14 letter tiles. Therefore, the probability of choosing a T from here is:

`(2)/(14)\rightarrow(1)/(7)`

Now, the probability that she will select the letter E first and the letter T second is:

`(1)/(5)\cdot(1)/(7)=(1)/(35)\rightarrow0.0286`

Or about 3%