A bowl contains 8 marbles:
3 red, 2 blue, 1 white, and 2 green. If 3 marbles are randomly selected without replacement, what is the probability that no green marble is selected?
I don't know how to do probability.
No green? that means
Pr(6/8)*(5/7)(4/6)
check my thinking. There are initially six non green, our of 8 marbles, then there are 5 out of 7, and on the third draw, 4 of 6 are non green.
There are many harder ways to do this.
To calculate the probability of not selecting any green marble, we need to find the total number of outcomes when 3 marbles are selected from the bowl without replacement, and the number of favorable outcomes where no green marble is selected.
Step 1: Find the total number of outcomes
When selecting 3 marbles without replacement, the total number of outcomes can be calculated using the combination formula. The formula for the number of combinations is:
nCr = n! / (r! * (n-r)!)
Where n is the total number of marbles and r is the number of marbles selected. In this case, we have 8 marbles and we are selecting 3, so the total number of outcomes is:
8C3 = 8! / (3! * (8-3)!)
= 8! / (3! * 5!)
= (8 * 7 * 6) / (3 * 2 * 1)
= 56
So, there are 56 possible outcomes when selecting 3 marbles without replacement.
Step 2: Find the number of favorable outcomes
To find the number of favorable outcomes where no green marble is selected, we need to consider the marbles other than green. In this case, we have 3 red, 2 blue, and 1 white marble. To find the number of combinations without any green marble, we sum up the combinations for these marbles:
(3C3) + (2C3) + (1C3) = 1 + 0 + 0 = 1
So, there is only 1 favorable outcome where no green marble is selected.
Step 3: Calculate the probability
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of outcomes:
P(No green marble) = number of favorable outcomes / total number of outcomes
= 1 / 56
Therefore, the probability of not selecting any green marble when 3 marbles are randomly selected without replacement is 1/56.