A bag of marbles contains 5 brown, 6 yellow, 4 blue, 3 green and 2 orange.
What is the probability of:
a) getting 3 yellow marbles, if 3 are taken at a time?
b) getting 1 brown and 2 orange marbles, if 3 are taken at a time?
a= 6/20* 5/19* 4/18
b=5/20* 2/19* 1/18
a) There is 20 marbles Total, 6 Yellow. The p(3 yellow) =
6/20 * 5/19 * 4/18 = 1/57
Or
(6 C 3)/(20 C 3)
To explain this, you have 6 yellow marbles and 20 total. So 1st pick is prob of 6/20. Now there is 5 yellow marbles left and 19 total. So the prob to pick a 2nd yellow marble is 5/19. Now there is only 4 yellow marbles left and 18 total marbles. Last pick then is 4/18.
b)
5/20 * 2/19 * 1/18 = 1/684
or
(5 C 1)*(2 C 2)/(20 C 3)
To calculate the probability, you need to determine the number of favorable outcomes (the number of ways the desired event can occur) and the total number of possible outcomes.
a) Probability of getting 3 yellow marbles, if 3 are taken at a time:
To find the probability, we will use the formula:
Probability = (Number of favorable outcomes) / (Number of possible outcomes)
Number of favorable outcomes:
We want to select 3 yellow marbles from a bag that contains 6 yellow marbles.
So, using combination, we can calculate the number of ways to choose 3 yellow marbles from 6:
Number of favorable outcomes = C(6, 3) = 6! / (3! * (6-3)!) = 20
Number of possible outcomes:
We have a total of 20 marbles in the bag.
So, using combination, we can calculate the number of ways to choose any 3 marbles from the 20:
Number of possible outcomes = C(20, 3) = 20! / (3! * (20-3)!) = 1140
Now we can calculate the probability:
Probability = Number of favorable outcomes / Number of possible outcomes
Probability = 20 / 1140 = 1 / 57
Therefore, the probability of getting 3 yellow marbles, if 3 are taken at a time, is 1/57.
b) Probability of getting 1 brown and 2 orange marbles, if 3 are taken at a time:
Number of favorable outcomes:
We want to select 1 brown marble and 2 orange marbles from a bag that contains 5 brown and 2 orange marbles.
Using combination, we can calculate the number of ways to choose 1 brown and 2 orange marbles:
Number of favorable outcomes = C(5, 1) * C(2, 2) = (5! / (1! * (5-1)!) * (2! / (2! * (2-2)!)) = 5 * 1 = 5
Number of possible outcomes:
We have a total of 20 marbles in the bag, and we want to select any 3 marbles.
So, using combination, we can calculate the number of ways to choose any 3 marbles from the 20:
Number of possible outcomes = C(20, 3) = 20! / (3! * (20-3)!) = 1140
Now we can calculate the probability:
Probability = Number of favorable outcomes / Number of possible outcomes
Probability = 5 / 1140 = 1 / 228
Therefore, the probability of getting 1 brown and 2 orange marbles, if 3 are taken at a time, is 1/228.