A box contains 3 red marbles, 6 blue marbles, and 1 white marble. The marbles are selected at random, one at a time, and are not replaced. Find the probability.
P(red and blue and blue)
Please help me
10 total marbles
3/10 red
1/9 white (since the marble isn't replaced)
So, 3/10 x 1/9 = 1/30
Probability questions
To calculate the probability of drawing a red marble, followed by two blue marbles, without replacement, we need to calculate the probability at each step.
Step 1: Probability of drawing a red marble (3 red marbles out of a total of 10 marbles):
P(red) = 3/10
Step 2: Probability of drawing a blue marble (6 blue marbles remaining out of a total of 9 marbles):
P(blue) = 6/9
Step 3: Probability of drawing another blue marble (5 blue marbles remaining out of a total of 8 marbles):
P(blue) = 5/8
To find the probability of all three events happening in sequence, we multiply the individual probabilities together:
P(red and blue and blue) = P(red) × P(blue) × P(blue)
= (3/10) × (6/9) × (5/8)
= 90/720
= 1/8
Therefore, the probability of drawing a red marble, followed by two blue marbles, without replacement, is 1/8 or approximately 0.125.
To find the probability of selecting a red marble, followed by two blue marbles, you need to calculate the individual probabilities and then multiply them together.
Step 1: Determine the probability of selecting a red marble.
In the box, there are a total of 10 marbles. Since there are 3 red marbles, the probability of selecting a red marble on the first draw is 3/10.
Step 2: Determine the probability of selecting a blue marble on the second draw.
After selecting a red marble, there are now 9 remaining marbles. Since there are 6 blue marbles, the probability of selecting a blue marble on the second draw is 6/9.
Step 3: Determine the probability of selecting another blue marble on the third draw.
After selecting a red marble and then a blue marble, there are now 8 remaining marbles. Since there are still 6 blue marbles left, the probability of selecting another blue marble on the third draw is 6/8.
Step 4: Multiply the individual probabilities together.
To get the probability of selecting a red and then two blue marbles, you multiply the individual probabilities together:
(3/10) x (6/9) x (6/8) = 9/40
Therefore, the probability of selecting a red marble first, followed by two blue marbles, is 9/40.