Each soccer player gets 4 jerseys red, yellow, white and green. A player randomly draws 2 jerseys each from the bag. The first jersey is not placed back in the bag.
A. What is the probability of first drawing a white and then a green jersey?
We (1) draw a white AND (2) then draw a green.
We start with this set of 16
R, R, R, R, Y, Y, Y, Y, W, W, W, W, G, G, G, G
(1) We can draw a white any of 4 ways out of 16. That's a probability of 
, which reduces to 
,
AND then that leaves this set of 15:
R, R, R, R, Y, Y, Y, Y, W, W, W, G, G, G, G
(2) We can then draw a green one any of 4 ways out of 15. That's a probability of 
.
That's all we wanted to do. Since the big word between 1 and 2 is AND, we multiply those probabilities:
Answer
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B. What is the probability of drawing a red and yellow jersey in any order?
What is the probability of first drawing a white and then a green jersey?
We (1) draw a red AND (2) then draw a yellow OR we (3) draw a yellow AND (4) then draw a red.
We start with this set of 16
R, R, R, R, Y, Y, Y, Y, W, W, W, W, G, G, G, G
(1) We can draw a red any of 4 ways out of 16. That's a probability of , which reduces to ,
AND then that leaves this set of 15:
R, R, R, Y, Y, Y, Y, W, W, W, W, G, G, G, G
(2) We can then draw a yellow any of 4 ways out of 15. That's a probability of .
OR
We start with this set of 16
R, R, R, R, Y, Y, Y, Y, W, W, W, W, G, G, G, G
(1) We can draw a yellow any of 4 ways out of 16. That's a probability of , which reduces to ,
AND then that leaves this set of 15:
R, R, R, R, Y, Y, Y, W, W, W, W, G, G, G, G
(2) We can then draw a red one any of 4 ways out of 15. That's a probability of .
Red AND yellow OR yellow AND red
AND means to multiply and OR means to add:
Answer
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C. What is the probablity of not drawing a red jersey?
We (1) draw a non-red AND (2) then draw another non-red.
We start with this set of 16
R, R, R, R, non-R, non-R, non-R, non-R, non-R, non-R, non-R, non-R, non-R, non-R, non-R, non-R
(1) We can draw a non-red any of 12 ways out of 16. That's a probability of 
, which reduces to 
,
AND then that leaves this set of 15:
R, R, R, R, non-R, non-R, non-R, non-R, non-R, non-R, non-R, non-R, non-R, non-R, non-R
(2) We can then draw a non-red any of 11 ways out of 15. That's a probability of 
.
That's all we wanted to do. Since the big word between 1 and 2 is AND, we multiply those probabilities:
Answer
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D. What is the probablity of having a white or red jersey after the second draw?
This requires finding the probability of the complenment event, and
then subtracting from 1
COMPLEMENT EVENT:
(1) Drawing a non-white-non-red AND (2) then drawing another non-white-non-red
We start with this set of 16
R, R, R, R, W, W, W, W, non-R-non-W, non-R-non-W, non-R-non-W, non-R-non-W, non-R-non-W, non-R-non-W, non-R-non-W, non-R-non-W
(1) We can draw a non-red-non-white any of 8 ways out of 16. That's a probability of 
, which reduces to 
,
AND then that leaves this set of 15:
R, R, R, R, W, W, W, W, non-R-non-W, non-R-non-W, non-R-non-W, non-R-non-W, non-R-non-W, non-R-non-W, non-R-non-W
(2) We can draw a non-red-non-white any of 7 ways out of 15. That's a probability of 
.
Answer to COMPLEMENT event:
Answer to DESIRED event:
Edwin
