Suppose a jar contains 138 red marbles and 153 blue marbles.  If you reach in the jar and pull out 2 marbles at random, find the probability that both are red. (Enter your answer as a decimal rounded to 2 places if necessary)

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter6: Ratio, Proportion, And Probability
Section6.7: Probability And Odds
Problem 1C
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Suppose a jar contains 138 red marbles and 153 blue marbles.  If you reach in the jar and pull out 2 marbles at random, find the probability that both are red.

(Enter your answer as a decimal rounded to 2 places if necessary)

Expert Solution
Step 1
138 + 153 = 291 marbles in total.
At our first pull, there is an 138/291 chance that a red will be pulled--the number of red out of the total number.
At the second pull there is a 137/290 chance that the second marble will be red as well--how many red/total are still in there.
 
From here, we multiply our two fractions together:
138/291 * 137/290
 
We can do a little bit of simplifying first; 10 and 291 both have a 2 in common:
138/13 * 5/290
 
Now we multiply our numerators (138 *5) and denominators (13 * 290)
 
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