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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?

Respuesta :

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:

[tex]\frac{3}{15}\rightarrow\frac{1}{5}[/tex]

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

[tex]\frac{2}{14}\rightarrow\frac{1}{7}[/tex]

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

[tex]\frac{1}{5}\cdot\frac{1}{7}=\frac{1}{35}\rightarrow0.0286[/tex]

Or about 3%

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