Twenty marbles are in a bag. There are 5 green marbles, 9 blue marbles, and the rest are red. Two marbles are drawn at random without placement. Find the probability that neither is blue
To find the probability that neither of the two marbles drawn from the bag is blue, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Step 1: Determine the total number of possible outcomes.
In this case, there are 20 marbles in the bag, so there are 20 possible choices for the first marble drawn. After the first marble is drawn, there are 19 marbles left for the second draw. Therefore, the total number of possible outcomes is 20 * 19 = 380.
Step 2: Determine the number of favorable outcomes.
We want to find the probability that neither of the two marbles drawn is blue. To do this, we need to count the number of ways to choose two marbles from the 20 without choosing any blue marbles.
There are 5 green marbles, so there are 5 choices for the first non-blue marble drawn. After the first non-blue marble is drawn, there are 4 green marbles left for the second draw. Therefore, there are 5 * 4 = 20 favorable outcomes (ways to draw two non-blue marbles).
Step 3: Find the probability.
Finally, the probability is given by the number of favorable outcomes divided by the total number of possible outcomes:
Probability = Favorable outcomes / Total outcomes
Probability = 20 / 380
Probability = 1 / 19 (approximately 0.0526 or 5.26%)
Therefore, the probability that neither of the two marbles drawn is blue is 1/19 or approximately 0.0526.
This is the same as both are either red or green.
red = (20-5-9)/20
green = 5/20
Either-or probabilities are found by adding the individual probabilities. This is for one choice.
But you are looking fro two choices. If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.