PRObability. Maths HELP!!?

Question

1, We have 15 marbles in a bag: 5 red, 4 blue, 3 yellow, 2 green, and 1 purple. We randomly pull two
marbles, with replacement. Find the probability of each of the following events.
(a) We pull two red marbles.
(b) We pull a red marble first, and then a green marble.
(c) We pull a red and a green marble. (Not necessarily in this order.)
(d) We pull no blue marble.
(e) We pull at least one blue marble.
(f) We pull two marbles of the same color.
(g) We pull two marbles of different color.

Answer 1

Hi,

a) The odds of pulling red are 5 out of 15 or 1/3 ( I'll always reduce after this) each time, so 1/3 x 1/3 = 1/9

b) Red first 1/3 followed by green, 2/15. Multiplying these, 1/3 x 2/15 = 2/45

c) Red first 1/3 followed by green, 2/15. Multiplying these, 1/3 x 2/15 = 2/45 BUT, you could also have Green first 2/15 followed by red, 1/3. Multiplying these, 2/15 x 1/3 = 2/45
Adding these together 2/45 + 2/45 = 4/45 for red green in either order.

d) Non-blue are 11 of 15. So 11/15 on first try and 11/15 on second try toget 11/15 x 11/15 = 121/225

e) First one blue 4/15 followed by one non-blue 11/15 to get 4/15 x 11/15 = 44/225 If you pulled the non-blue first followed by blue that would be another 44/225.
If you pulled both blue, 4/15 x 4/15 = 16/225
Altogether that's 44/225 + 44/225 + 16/225 = 104/225

f) No reducing until the end on this one...
Two red 25/225
Two blue 16/225
Two yellow 9/225
Two green 4/225
Two purple 1/225
Altogether, 25/225 + 16/225 + 9/225 + 4/225 + 1/225 =
55/225 which reduces to 11/45

g) No reducing until the end on this one...
(Red x non-red) = (5/15 x 10/15) = 50/225
(Blue x non-blue) = (4/15 x 11/15) = 44/225
(Yellow x non-yellow) = (3/15 x 12/15) = 36/225
(Green x non-green) = (2/15 x 13/15) = 26/225
(Purple x non-purple) = (1/15 x 14/15) = 14/225

The total is 50/225 + 44/225 + 36/225 + 26/225 + 14/225 =
170/225 or 34/45

Notice that the probabilities of getting different colors on part g and the same colors on part f add up to 1, because those are the only things that could happen! 11/45 + 34/45 = 1

I hope this helps.

Answer 2

a) 2 red marbles
5/15 x 5/15 =1/9
b) red then green
5/15 x 2/15 = 2/45
c)red and green (any order)
2/45 + 2/45 (red then green OR green then red)
4/45
d) No blue marble
11/15 x 11/15 = 121/225
e) At least one blue:
1-121/255=104/255
f) 2 marbles same colour
(5/15)^2+(4/15)^2+(3/15)^2
+(2/15)^2+(1/15)^2
work that out yourself
g) simply 1-the above answer.

Hope this helps you.

Answer 3

Firstly calculate the probabilities of each colour.

5/15 for red, 4/15 for blue, etc.

For each of the questions calculate the probability from the law of independent events
P(A and B) = P(A)*P(B)
So for question a) P(two reds)=(5/15)*(5/15)
=(1/3)*(1/3)
=1/9

Carry on.....

Answer 4

It solve by "n!"
If u don't know,
go find another way!
any way it's too easy think about it

5 X 4 X 3 X 2 X 1 = 120 position

Answer 5

a) 2/15
b) 1/15 1/15
c) 2/15
d) 11/15
e) 2/15
f) 2/15
g) 2/15