How many times will she draw a Q?

Question

There are 100 letter tiles in a Scrabble game and only one "Q."  If Ann draws her 7 tiles first, what is the probability she will draw the "Q" tile?

Answer 1

Hi Paula,

 

With probability questions like this, where we want to find out the probability of something happening during a particular number of trials, it's often easier to instead determine the probability that something DOESN'T happen during those attempts.

 

    Since the P(event occurring) + P(event not occurring) = 1

 

    P(event occurring) = 1 - P(event not occurring)

 

In order to draw seven tiles WITHOUT drawing the Q tile, the probability would be:

 

    (99/100)*(98/100)*(97/100)*(96/100)*(95/100)*(94/100)*(93/100) ≈ .750

 

So the probability of drawing the Q tile as one of those 7 initial tiles would be 1 - .750 = .250  or 25.0%