Suppose a jar contains 5 red marbles and 33 blue marbles. If you reach in the jar and pull out 2 marbles at random without replacement, find the probability that both are red.
(5/38)(4/37) = ...
To find the probability of pulling out 2 red marbles, we first need to determine the total number of marbles in the jar after pulling out the first one.
Initially, there are 5 red marbles and 33 blue marbles, making a total of 38 marbles in the jar.
After removing one marble without replacement, there will be 37 marbles left in the jar, since we did not put the first marble back.
The probability of picking a red marble as the first marble is (5 red marbles / 38 total marbles) = 5/38.
Now, for the second marble, there will be 4 red marbles remaining in the jar, as we have already pulled out one red marble.
Since there is one less marble now, the total number of marbles is now 37 - 1 = 36.
The probability of picking a second red marble without replacement is (4 red marbles / 36 total marbles) = 4/36.
To find the probability of both marbles being red, we can simply multiply the probabilities of picking the first and the second red marbles together:
(5/38) * (4/36) = 20/1368.
Simplifying the fraction, we get the probability that both marbles are red as 5/342.
So, the probability of pulling out two red marbles is 5/342.