given a jar contains four marbles, each a different color: red, blue, green, and yellow. If you draw two marbles from the jar, one after another, replacing the first before drawing the second,what is the probability of getting a red marble on the first draw and a green marble on the second draw?
Since there is replacement of the marbles, the two draws are independent. The joint probability of two independent events is the product of the individual probabilities.
P(R)=1/4
P(G)=1/4
P(R∩G)=(1/4)(1/4)=1/16
To determine the probability of getting a red marble on the first draw and a green marble on the second draw, we need to calculate the probability of each event separately and then multiply them together.
Step 1: Calculate the probability of drawing a red marble on the first draw.
Since there are 4 marbles in total, and we are replacing the first marble before drawing the second one, the probability of getting a red marble on the first draw is 1/4.
Step 2: Calculate the probability of drawing a green marble on the second draw.
Again, since there are 4 marbles in total and we replaced the first marble, the probability of getting a green marble on the second draw is also 1/4.
Step 3: Multiply the probabilities together.
To find the overall probability, we need to multiply the individual probabilities found in step 1 and step 2:
P(red first and green second) = P(red first) * P(green second)
= 1/4 * 1/4
= 1/16
Therefore, the probability of drawing a red marble on the first draw and a green marble on the second draw is 1/16.