Need help with this one (Probability)

Question

Jen has a bag of 5 red, 6 blue, 10 orange, and 4 brown jawbreakers. She grabs one jawbreaker, eats it, and then grabs a second.

 

 

 

What is the probability that she grabbed a red jawbreaker and then a brown one?

Answer 1

Hi Sarah,

 

The probability of picking any particular color will be the ratio of the number of jawbreakers of that color to the total number of jawbreakers in the bag.

 

Before Jen eats the jawbreakers, what is the number of red jawbreakers in the bag and what is the total number of jawbreakers in the bag?

 

After she eats the first jawbreaker, how many jawbreakers are left in the bag and how many of these jawbreakers are brown?

 

The probability of grabbing a red jawbreaker and then a brown jawbreaker is the product of the two ratios above.   

Answer 2

We need to find each probability separately and then multiply them together.

 

To find the probability of the first situation (grabbing a red jawbreaker), simply make a ratio out of the number of desired (5 red) over the possible (25 total).  So, the probability of drawing a red jawbreaker would be 5/25 (or 1/5 when simplified). 

 

To find the probability of the second situation (grabbing a brown one), make a ratio of the number of desired (4 brown) over the possible (now 24 total since the first red one was eaten).  So, the probability of drawing a brown jawbreaker would be 4/24 (or 1/6 when simplified). 

 

Now, take the two simplified ratios and multiply them together: 1/5 X 1/6 = 1/30.  Therefore, the probability of grabbing a red one THEN a brown one is 1/30.

 

To make this probability a percentage, simply turn the fraction 1/30 into a division statement.  1 divided by 30 is .0333, so you would say the probability is about 3%.