An experiment consists of drawing a marble out of a bag, observing the color, and then placing it back in the bag. Suppose the experiment is repeated 75 times, with the following results:
red 38
blue 23
green 11
yellow 3
What is the probability of drawing two yellow marbles in a row?
To determine the probability of drawing two yellow marbles in a row, we need to consider the probability of drawing a yellow marble on the first draw and then the probability of drawing a yellow marble again on the second draw.
The probability of drawing a yellow marble on the first draw is given by the number of yellow marbles divided by the total number of marbles:
P(Yellow on First Draw) = 3/75 = 1/25
Since the marbles are placed back in the bag after each draw, the probability of drawing a yellow marble on the second draw is the same as the probability on the first draw:
P(Yellow on Second Draw) = 1/25
To calculate the probability of both events occurring, we multiply the individual probabilities:
P(Yellow on First Draw and Yellow on Second Draw) = P(Yellow on First Draw) × P(Yellow on Second Draw)
= (1/25) × (1/25)
= 1/625
Therefore, the probability of drawing two yellow marbles in a row is 1/625.
To find the probability of drawing two yellow marbles in a row, we need to know the total number of marbles in the bag.
From the given information, we know that there are 75 draws in total. However, we don't know the specific number of marbles in the bag. To find the probability, we need to know the total number of marbles in the bag before any draws were made.
If we assume there were n total marbles in the bag before the experiment started, then the probability of drawing a yellow marble on the first draw would be 3/n, as there are 3 yellow marbles.
After the first yellow marble is drawn, it is placed back into the bag, so there are still n marbles in the bag. The probability of drawing a yellow marble on the second draw would again be 3/n since we assume the number of marbles in the bag does not change between draws.
To find the probability of drawing two yellow marbles in a row, we need to multiply the probabilities of each draw. So the probability can be calculated as (3/n) * (3/n) = 9/n^2.
Without knowing the value of n, we cannot determine the exact probability.