a jar contains two red and five yellow marbles. A marble is drawn at random and then replaced. A second draw is made at random. find the probability that both marbles are red?
(2/7)*(2/7) = 4/49
To find the probability that both marbles drawn are red, we need to determine the probability of drawing a red marble on the first draw, and then multiply that by the probability of drawing another red marble on the second draw (since the marble is replaced after each draw).
Let's break down the steps to calculate this:
Step 1: Determine the probability of drawing a red marble on the first draw.
There are a total of 2 red marbles out of 7 marbles in the jar. Therefore, the probability of drawing a red marble on the first draw is 2/7.
Step 2: Determine the probability of drawing a red marble on the second draw.
Since the marbles are replaced after each draw, the probability of drawing a red marble on the second draw is also 2/7.
Step 3: Multiply the probabilities from steps 1 and 2.
To find the probability of both events happening (drawing a red marble on the first draw and a red marble on the second draw), we multiply the probabilities from step 1 and step 2 together:
P(both marbles are red) = (2/7) * (2/7).
Calculating this, we get:
P(both marbles are red) = 4/49.
Therefore, the probability of drawing two red marbles is 4/49.