Probabilty question: where m i wrong??

[him1985]

Q. A certain deck of cards contains 2 blue cards, 2 red cards, 2 yellow cards, and 2 green cards. If two cards are randomly drawn from the deck, what is the probability that they will both are not blue?

A. 15/28

B. 1/4

C. 9/16

D. 1/32

E. 1/16


We can have two approches here:
(1). direct find probabilty that both balls are not blue.
6/8 * 5/7 = 15/28

(2). We can find the prob. that both balls are blue and can substract from 1

1- (2/8*1/7) = 27/28

I am getting two different answer but according to probability rule i should get answer same in both way. Please help....

[rijul007]

Q. A certain deck of cards contains 2 blue cards, 2 red cards, 2 yellow cards, and 2 green cards. If two cards are randomly drawn from the deck, what is the probability that they will both are not blue?

A. 15/28

B. 1/4

C. 9/16

D. 1/32

E. 1/16


We can have two approches here:
(1). direct find probabilty that both balls are not blue.
6/8 * 5/7 = 15/28

(2). We can find the prob. that both balls are blue and can substract from 1

1- (2/8*1/7) = 27/28

I am getting two different answer but according to probability rule i should get answer same in both way. Please help....

Analyze the appraoches yourself, and answer this ques for each appraoch
does the computed probability include the selection of one blue and one green?

Did you see the difference?

[LalaB]

him1985,

the probability that both are not blue=1-(probability that one or both are blue)

the probability that they will both are not blue=1-(2C2+2C1*6C1)/8C2=1-13/28=15/28

One more approach-

6C2/8C2=15/28

[ronnie1985]

No blue = 6C2
2 balls = 8C2
P = 6c2/8C2 = 15/28.

[him1985]

him1985,

the probability that they will both are not blue=1-(2C2+2C1*6C1)/8C2=1-13/28=15/28

LalaB: Can you please elaborate this calculation. Probability that both are blue =(2C2+2C1*6C1)/8C2

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him1985,

the probability that they will both are not blue=1-(2C2+2C1*6C1)/8C2=1-13/28=15/28

LalaB: Can you please elaborate this calculation. Probability that both are blue =(2C2+2C1*6C1)/8C2

I can elaborate.
selecting 2 blue out of 2 blue =2C2=1
selecting 1 blue out of 1 blue and selecting any other out of 6 different=2C1*6C1=12

So Prob is =1-13/8C2=1-13/28=15/28