You are going to draw two candy bars from a large bag containing 23 Snickers bars and 7 Twix bars. What is the probability that both candy bars you draw from...

Question

You are going to draw two candy bars from a large bag containing 23 Snickers bars and 7 Twix bars. What is the probability that both candy bars you draw from the bag are Snickers?

Answer 1

P(first Snickers) = 23/30

(now there are 29 remaining, w/o replacement) so P(Snickers) is 22/29.

 

Multiply these two different probabilities to compute P(2 consecutive Snickers).

Answer 2

Here we have a probability question involving one event (drawing a Snickers on the first choice) AND a second event (drawing a Snickers on the second choice). In these kinds of problems we want to MULTIPLY the two probabilities together.

 

For the first choice, the probability of drawing a Snickers is 23/30 (the number of Snickers / the number of total candy bars).

 

For the second choice, there are only 29 candy bars left, 22 of which are Snickers. So that probability is 22/29.

 

The probability of BOTH things happening is their product 23/30 * 22/29 = 506/870 = 253/435.