A jar contains 2 red marbles, 3 green marbles, 4 blue marbles, and 5 yellow marbles. Two marbles are drawn in succession, without replacement. The probability that neither is yellow?
find prob of getting two yellows
= (5/14)(4/13) = 10/91
so prob that neither is yellow = 1-10/91 = 81/91
To find the probability that neither of the two marbles drawn is yellow, we need to determine the total number of possible outcomes and the number of favorable outcomes.
First, let's find the total number of possible outcomes. We need to draw two marbles without replacement, which means that the number of potential outcomes will decrease with each draw. For the first draw, there are 14 marbles in total to choose from. After the first marble is drawn, there are 13 marbles left for the second draw. Therefore, the total number of possible outcomes is:
Total number of possible outcomes = 14 * 13 = 182
Now, let's find the number of favorable outcomes, which refers to the scenarios where neither of the two marbles is yellow. Since we don't want yellow marbles, we need to consider the other colors.
There are 2 red marbles, 3 green marbles, and 4 blue marbles. For the first draw, there are 9 favorable marbles out of 14. After one marble is drawn, there will be 8 favorable marbles left out of 13 for the second draw. Therefore, the number of favorable outcomes is:
Number of favorable outcomes = 9 * 8 = 72
Now, let's calculate the probability:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 72 / 182
Probability ≈ 0.3956
Therefore, the probability that neither of the two marbles drawn is yellow is approximately 0.3956.