A box contains 4 red pencils, 3 blue pencils, and 3 yellow pencils. What is
the probability that a student randomly selects a blue pencil, keeps it, then a second student randomly selects a yellow
pencil?
A. 1/10
B. 3/10
C. 6/10
D. 9/10
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
3/10 * 3/9 = ?
Well, that's quite a colorful situation! Let's see how we can clown around with probabilities here.
First, let's find the probability of the first student selecting a blue pencil. There are a total of 4 + 3 + 3 = 10 pencils in the box, and 3 of them are blue. So, the probability of picking a blue pencil is 3/10.
Now, for the second student to randomly select a yellow pencil, after the first student has already taken a blue pencil, there are 3 yellow pencils left in the box. Since the first student doesn't put the blue pencil back, there are now 9 pencils left in total. Therefore, the probability of the second student selecting a yellow pencil is 3/9.
Now, to find the probability of both events happening together (first student picks blue and second student picks yellow), we multiply the probabilities of each event. So, the overall probability is (3/10) * (3/9) = 9/90 = 1/10.
So, the answer is A. 1/10. It looks like the clowns have some mathematical tricks up their sleeves after all!
To find the probability of these events happening, we need to multiply the probabilities of each event.
Step 1: Calculate the probability of the first student randomly selecting a blue pencil:
There are a total of 4 red pencils, 3 blue pencils, and 3 yellow pencils. The probability of selecting a blue pencil on the first draw is 3/(4+3+3) = 3/10.
Step 2: Calculate the probability of the second student randomly selecting a yellow pencil:
After the first student selects a blue pencil, there are now only 3 blue pencils, 4 red pencils, and 3 yellow pencils left. The probability of selecting a yellow pencil on the second draw is 3/(3+4+3) = 3/10.
Step 3: Multiply the probabilities from Step 1 and Step 2:
The probability of the first student selecting a blue pencil AND the second student selecting a yellow pencil is (3/10) * (3/10) = 9/100.
Therefore, the probability that a student randomly selects a blue pencil, keeps it, and then a second student randomly selects a yellow pencil is 9/100.
The correct answer choice is not provided in the options, as it should be 9/100.
To find the probability that a student randomly selects a blue pencil and then a second student randomly selects a yellow pencil, we need to determine the total number of possible outcomes and the number of favorable outcomes.
First, let's find the total number of possible outcomes. The first student can select any of the 10 pencils in the box, and after that, the second student can select any of the remaining 9 pencils. So, the total number of possible outcomes is 10 * 9 = 90.
Next, let's find the number of favorable outcomes. The first student needs to select one of the 3 blue pencils, and then the second student needs to select one of the 3 yellow pencils. So, the number of favorable outcomes is 3 * 3 = 9.
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
= 9 / 90
= 1 / 10
Therefore, the probability that a student randomly selects a blue pencil and then a second student randomly selects a yellow pencil is 1/10.
Therefore, option A (1/10) is the correct answer.