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.
A. The probability of choosing a yellow, green, red, or blue marble is 1. (True, since these are the only options)
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, the probability of choosing a yellow marble is actually higher)
C. The probability of choosing a green marble is 0.25. (False, since there are 5 green marbles out of 20 total, the probability of choosing a green marble is actually 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)
Let's break down each statement one by one:
A. The probability of choosing a yellow, green, red, or blue marble is 1.
To find the probability, we need to consider the total number of marbles in the bag (20) and the number of marbles of each color. Since there are marbles of all four colors in the bag, statement A is true.
B. The probability of choosing a yellow marble is less than the probability of choosing a blue marble.
Again, we need to consider the total number of marbles and the number of marbles of each color. There are 2 yellow marbles and 1 blue marble. So the probability of choosing a yellow marble is 2/20 or 0.1, and the probability of choosing a blue marble is 1/20 or 0.05. Therefore, statement B is false.
C. The probability of choosing a green marble is 0.25.
To find the probability, we need to consider the total number of marbles and the number of green marbles. There are 5 green marbles, so the probability of choosing a green marble is 5/20 or 0.25. Thus, statement C is true.
D. The probability of choosing a black marble is zero.
There are no black marbles mentioned in the question. Since there are no black marbles in the bag, the probability of choosing a black marble is indeed zero. Therefore, statement D is true.
In summary, the true statements are:
A. The probability of choosing a yellow, green, red, or blue marble is 1.
C. The probability of choosing a green marble is 0.25.
D. The probability of choosing a black marble is zero.