A bag has 6 blue marbles, 4 red marbles, and 2 green marbles. Two marbles are randomly chosen without replacement. What is the probability that both marbles picked are blue? Answer options with 5 options A. StartFraction 1 over 6 EndFraction B. StartFraction 2 over 24 EndFraction C. StartFraction 5 over 22 EndFraction D. StartFraction 1 over 4 EndFraction E. StartFraction 1 over 3 EndFraction
Question
A bag has 6 blue marbles, 4 red marbles, and 2 green marbles. Two marbles are randomly chosen without replacement.
What is the probability that both marbles picked are blue?
Answer options with 5 options A. StartFraction 1 over 6 EndFraction
B. StartFraction 2 over 24 EndFraction
C. StartFraction 5 over 22 EndFraction
D. StartFraction 1 over 4 EndFraction
E. StartFraction 1 over 3 EndFraction
Solution
To solve this problem, we need to calculate the probability of drawing a blue marble twice in a row from the bag.
Step 1: Calculate the total number of marbles in the bag. This is 6 (blue) + 4 (red) + 2 (green) = 12 marbles.
Step 2: Calculate the probability of drawing a blue marble on the first draw. This is the number of blue marbles (6) divided by the total number of marbles (12). So, the probability is 6/12 = 1/2.
Step 3: Now, we need to calculate the probability of drawing a blue marble on the second draw. But, since we've already drawn one blue marble and haven't replaced it, there are now only 5 blue marbles left, and the total number of marbles is 11. So, the probability is 5/11.
Step 4: The probability of both events happening (drawing a blue marble twice in a row) is the product of the probabilities of each event. So, we multiply the probabilities from Step 2 and Step 3 together: (1/2) * (5/11) = 5/22.
So, the correct answer is C. StartFraction 5 over 22 EndFraction.
Similar Questions
Inside a bag, there are 3 red, 4 green and 3 blue marbles. If you were to pick out two marbles without looking, what is the probability that neither of the selected marbles is blue?
Allison has a pouch of 6 pink marbles, 4 blue marbles, and 8 white marbles.What is the probability that the first marble is blue and the second marble is white if replacement is allowed?*1 pointA. 0.078B. 0.099C. 0.104D. 0.148
A bag contains 3 black, 4 red, 3 yellow, and 2 green marbles. What is the probability of drawing a black and then a red marble out of the bag without replacing the black marble before drawing the red marble? Answer options with 5 options A. StartFraction 1 over 144 EndFraction B. StartFraction 1 over 11 EndFraction C. StartFraction 1 over 12 EndFraction D. StartFraction 7 over 12 EndFraction E. StartFraction 27 over 44 EndFraction
Melissa has a bag that contains 6 red marbles, 8 yellow marbles, and 18 blue marbles. If she chooses one marble from the bag, what is the probability that the marble is not blue?A.B.C.D.
A bag contains 6 red marbles, 5 black marbles and 4 white marbles. Two marbles are drawn from the bag, one after the other, without replacement. If the first marble drawn is red, what is the probability that the second marble drawn is also red.
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.