a bag conatins 5 white marbles and 3 green marbles. find the probability of selecting each combination?

Question

a) 2 green and 1 white

b) 3 green and 2 white



thanks

Answer 1

a) there are 3 orders in which to get 2 green and 1 white: GGW, GWG, WGG. the probability of getting 2 green and 1 white regardless of order is 3/8 * 2/7 * 5/6 = 5/56. Multiply that by the 3 ways to get 2 green and 1 white is 15/56.

b) same concept.

Answer 2

a) select 3 out of 8. The possible combination is:
(8*7*6) / 3! = 56 ways

find the combination of selecting 2 green out of 3
(3*2) / 2 = 3

cobinattion of 1 white out of 5. It's 5
3*5 = 15
so the probability is 15/56

b) select 5 out of 8. The possible combination is
(8*7*6*5*4) / (5!) = 56 ways.

the combination of 3 green out of 3 is 1 way.
the combination of 2 white out of 5 is (5*4)/2 = 10
10 * 1 = 10

so the probability is 10/56 or 5/28

Answer 3

Below, the notation nCr = n!/{r!(n-r)!}

a)

Number of ways to get greens = 3C2 = 3 ( = 3!/(2!1!))
Number of ways to get whites = 5C1 = 5 ( = 5!/(1!4!))

Using the general counting rule, there are 3*5 = 15 ways to draw two green and one white.

Number of possible draws of three marbles = 8C3 = 56 ( = 8!/(3!5!))
Probability = 15/56

b)

Number of ways to get greens = 3C3 = 1
Number of ways to get whites = 5C2 = 10

Using the general counting principle, there are 1*10 = 10 ways to draw 3 greens and 2 white.

Number of possible ways to draw 5 marbles = 8C5 = 56
Probability = 1*10/56 = 10/56

edit: The above was assuming that the draws are made without replacement. If it is with replacement, then you would want to use the binomial distribution.

a) (3C2) * (3/8)^2 * (5/8)^1
=135/512
= 0.2637

b) (5C3) * (3/8)^3 * (5/8)^2
= 6750/32768
= 0.2060

edit: Some idiot gave me a thumbs down. Look, I teach statistics. I know my answer is right.

Everybody else had the same answer for the without replacement case. metsfan1990 gave an incorrect response for the with replacement case. That answer did not take the possible ways to rearrange the different colors. You need to use the binomial for that.

Answer 4

The total number of marbles in the bag is 8. Probability is the #success/#total. Order does not matter so we're talking about combinations, not permutations.

a) (3c2)(5c1) / (8c3) = 15/56

b) (3c3)(5c2) / (8c5) = 10/56

Answer 5

With or without replacement?

Without which I assume:

A. (3/8)(2/7)(5/6) = 5/56

B. (3/8)(2/7)(1/6)(5/5)(4/4) = 1/56

With replacement:

A. (3/8)^2 (5/8) = 45/512

B. (3/8)^3 (5/8)^2 = 0.0206

Answer 6

I assume you mean without replacement.

P(2G and 1W) = (3C2)(5C1) / (8C3) = 3*5/56 = 15/56

P(3G and 2W) = (3C3)(5C2) / (8C5) = 1*10/56 = 10/56 = 5/28

Answer 7

b