99. From a box containing 5 black marbles,8 pink marbles, 6 white marbles, and 5 yellow marbles, Kim removed 4 marbles,one of which was black.If she removes one more marble at random,what is the probability that it will be black?
a. 1/6
b. 4/21
c. 1/5
d. 5/21
e. 1/4
please answer and explain
To determine the probability that the randomly selected marble will be black, we need to calculate the number of favorable outcomes (black marbles) and the total number of possible outcomes.
Given that out of the 4 marbles previously removed, one was black, we know that there are 3 black marbles remaining in the box.
The total number of marbles remaining in the box is:
5 black marbles + 8 pink marbles + 6 white marbles + 5 yellow marbles - 4 marbles removed = 20 marbles
Therefore, the probability of selecting a black marble on the next try is:
3 black marbles / 20 marbles
Simplifying the fraction, we get:
3/20
The final answer is:
b. 3/20
So the correct option is 3/20.
To find the probability of drawing a black marble from the box, we need to determine the number of favorable outcomes (black marbles) and the number of possible outcomes (total number of marbles).
Kim has already removed 4 marbles, and one of them was black. So, we know that there are now 4 black marbles left in the box.
The total number of marbles remaining in the box after Kim's removal is 5 (black) + 8 (pink) + 6 (white) + 5 (yellow) - 4 (removed) = 20.
Now, Kim will remove one more marble at random. Since we already know there are 4 black marbles left and a total of 20 marbles remaining, the probability of drawing a black marble can be calculated as:
Probability = Number of favorable outcomes / Number of possible outcomes
Probability = 4 / 20
Simplifying the fraction, we get:
Probability = 1 / 5
Therefore, the probability that the next marble Kim removes will be black is 1/5.
Therefore, the correct answer is option c: 1/5.