A bag contains different colored balls; 7 yellow, 3 red, and 6 green. I randomly select one ball, note its color, put it back in the bag, and select another ball. What is the probability that both balls I selected were green, P(GG)?
To find the probability of selecting two green balls, we need to consider the probability of selecting a green ball on the first draw and then the probability of selecting a green ball on the second draw.
The probability of selecting a green ball on the first draw is 6/16 because there are 6 green balls out of a total of 16 balls.
Since we put the first green ball back in the bag, the probability of selecting a green ball on the second draw is also 6/16.
To find the probability of both events happening, we multiply the probabilities: (6/16) * (6/16) = 36/256.
Therefore, the probability of selecting two green balls is 36/256, which simplifies to 9/64.
To find the probability that both balls selected are green (P(GG)), we need to divide the number of favorable outcomes by the number of possible outcomes.
Number of favorable outcomes:
Since we put the first ball back in the bag before selecting the second one, the probability of selecting a green ball for each draw remains the same. Therefore, the number of favorable outcomes is calculated as the product of the number of green balls (6) and the number of green balls (6) again, resulting in 6 * 6 = 36.
Number of possible outcomes:
In this case, the number of possible outcomes is equal to the total number of balls in the bag. We have 7 yellow balls, 3 red balls, and 6 green balls, resulting in a total of 7 + 3 + 6 = 16 balls.
Therefore, the probability that both balls selected are green (P(GG)) is calculated as:
P(GG) = Number of favorable outcomes / Number of possible outcomes
P(GG) = 36 / 16
P(GG) = 9 / 4
Therefore, the probability that both balls selected are green is 9/4, which can also be written as 2.25.
To find the probability of selecting two green balls (GG) from the bag, we need to calculate the probability of selecting a green ball on the first draw and a green ball again on the second draw.
First, let's find the probability of selecting a green ball on the first draw.
There are a total of 7 + 3 + 6 = 16 balls in the bag, out of which 6 are green. Therefore, the probability of selecting a green ball on the first draw is 6/16.
Now, we put the ball back in the bag, and since we're selecting randomly again, the number of balls and the number of green balls in the bag remain unchanged.
Similarly, the probability of selecting a green ball on the second draw is also 6/16.
To find the probability of both events happening, we multiply the probabilities together:
P(GG) = (6/16) * (6/16) = 36/256 = 9/64
Therefore, the probability that both balls you selected were green, P(GG), is 9/64.