Grace has 2 yellow balloons and 3 red balloons. Her brother, Caleb, is going to pop two of the balloons at random. What is the probability that he pops one of the yellow balloons and one of the red balloons?
prob(yellow, then red) = (2/5)(3/4) = 3/10
prob(red, then yellow) = 3/5(2/4) = 3/10
so prob(your event) = 6/10 = 3/5
Thanks Reiny!
To find the probability that Caleb pops one yellow balloon and one red balloon, we need to first determine the total number of ways Caleb can choose 2 balloons out of the 5 available.
The number of ways to choose 2 balloons out of 5 is given by the combination formula: nCr = n! / (r! * (n-r)!), where n is the total number of balloons and r is the number of balloons to be chosen.
In this case, n = 5 (total number of balloons) and r = 2 (number of balloons to be chosen).
Using the combination formula, we have:
nCr = 5! / (2! * (5-2)!) = 5! / (2! * 3!) = (5 * 4 * 3!) / (2 * 1 * 3!) = (5 * 4) / (2 * 1) = 10.
So, there are 10 possible ways for Caleb to choose 2 balloons out of the 5 available.
Now, let's determine the number of ways Caleb can choose one yellow balloon and one red balloon. Since there are 2 yellow balloons and 3 red balloons, Caleb can choose 1 yellow balloon out of 2 and 1 red balloon out of 3.
Using the multiplication principle, the number of ways Caleb can choose one yellow balloon and one red balloon is: 2 * 3 = 6.
Therefore, the probability that Caleb pops one yellow balloon and one red balloon is given by: desired outcomes / total outcomes = 6/10 = 3/5 = 0.6.
So, the probability is 0.6 or 60%.