You have a bag with 20 marbles: 2 yellow, 5 green, 12 red, and 1 blue. Which of the following statements are true? Select all that apply.
A.The probability of choosing a yellow, green, red, or blue marble is 1.
B.The probability of choosing a yellow marble is less than the probability of choosing a blue marble.
C. The probability of choosing a green marble is 0.25.
D.The probability of choosing a black marble is zero.
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A. The probability of choosing a yellow, green, red, or blue marble is 1. (True, since these are the only colors of marbles in the bag, and one of them is guaranteed to be chosen.)
B. The probability of choosing a yellow marble is less than the probability of choosing a blue marble. (False, since there is only one blue marble and two yellow marbles, so the probability of choosing a yellow marble is higher.)
C. The probability of choosing a green marble is 0.25. (False, since there are 5 green marbles out of 20 total, so the probability of choosing a green marble is 5/20 or 0.25.)
D. The probability of choosing a black marble is zero. (True, since there are no black marbles in the bag.)
Therefore, the correct statements are A and D.
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To determine which statements are true, we need to calculate the probability of each event:
A. The probability of choosing a yellow, green, red, or blue marble is 1.
To calculate the probability, we need to add up the probabilities of each event:
P(yellow) + P(green) + P(red) + P(blue)
= 2/20 + 5/20 + 12/20 + 1/20
= 20/20
= 1
So, statement A is true.
B. The probability of choosing a yellow marble is less than the probability of choosing a blue marble.
To compare the probabilities, we need to calculate them:
P(yellow) = 2/20
P(blue) = 1/20
Since 2/20 is less than 1/20, statement B is false.
C. The probability of choosing a green marble is 0.25.
P(green) = 5/20
= 1/4
So, statement C is false.
D. The probability of choosing a black marble is zero.
Since there are no black marbles in the bag, the probability is indeed zero.
So, statement D is true.
In summary, statements A and D are true.