In a bag, there are 6 black pens, 4 blue pens, and 5 red pens. If three pens are drawn without replacement, what is the probability that the first pen is black, the second pen is blue, and the third pen is red?
Question
In a bag, there are 6 black pens, 4 blue pens, and 5 red pens. If three pens are drawn without replacement, what is the probability that the first pen is black, the second pen is blue, and the third pen is red?
Solution
Sure, here's how you can calculate the probability:
Step 1: Calculate the total number of pens. We have 6 black pens, 4 blue pens, and 5 red pens. So, the total number of pens is 6 + 4 + 5 = 15 pens.
Step 2: Calculate the probability of drawing a black pen first. There are 6 black pens out of a total of 15 pens. So, the probability is 6/15.
Step 3: Now, one pen has been drawn, so there are only 14 pens left. Calculate the probability of drawing a blue pen next. There are 4 blue pens out of a total of 14 pens. So, the probability is 4/14.
Step 4: Now, two pens have been drawn, so there are only 13 pens left. Calculate the probability of drawing a red pen next. There are 5 red pens out of a total of 13 pens. So, the probability is 5/13.
Step 5: The final step is to multiply these three probabilities together to get the overall probability of drawing a black pen, then a blue pen, then a red pen. So, the overall probability is (6/15) * (4/14) * (5/13) = 0.033.
So, the probability that the first pen is black, the second pen is blue, and the third pen is red is 0.033 or 3.3%.
Similar Questions
A box contains 9 white 4 black and 7 red pens. Three pens are selected in succession without replacement. What is the probability if the first pen is red, second is black and third is also red
A bag contains 3 blue balls, 4 red balls and 5 vellow balls. Three balls are randomly drawn one by one withoutreplacement.given that the first ball is red and the second is yellow,find the probability that the thrid ball is yellow
A bag contains 3 red balls 5 black balls . Two balls are to be taken at random without replacement, from the bag. Find the probability that the two balls taken are of the same colour.
You have a bag containing 5 red markers, 6 green markers, and 4 blue markers. You reach into the bag, select 1 marker, replace it, and then select another marker. What is the probability that you selected a blue marker and then a green marker?
The bag has three red balls, five purple balls and eight blue balls. What is the probability that if two are picked at random with replacement, what is the probability that both are purple? Round your answer to four decimal placesA.0.0352B.0.3125C.0.0977D.0.0833
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.