probability 2?

Question

. If three persons are randomly selected , whats the probability that two were born on Monday and the other on Tuesday?

2. If Jack studies for tmr's test the prob. of getting a pass is 4/5 , if he doesnt study for it , the prob of getting a pass is 1/10. Given the prob. for Jack to study the test is 7/8 , find the prob. that he will fail the test .

YA HOO！知識＋管理員 · Accepted Answer

1.
First, select 2 persons which were born on Monday [ C(3,2) (1/7)² ]
Second, select 1 person which was born on Tuseday [ C(1,1) (1/7) ]

The probability
= C(3,2) (1/7)² C(1,1) (1/7)
= 3/343

2.
Condition 1：Jack studies for tmr's test and fail the test
The probability = (7/8)(1 - 4/5)

Condition 2：Jack doesn't studies for tmr's test and fail the test
The probability = (1 - 7/8)(1 - 1/10)

∴ The probability
= (7/8)(1 - 4/5) + (1 - 7/8)(1 - 1/10)
= 23/80

3.
Bag A contains black and white chess pieces.If one chess piece is drawn at random from the bag,the prob.of drawing a white chess piece and a black one are 2/3 and 1/3 respectively.
Bag B contains 6 white chess pieces and 8 black chess pieces.One chess piece is drawn at random from bag A and is put to Bag B,the one chess piece is drawn at random from Bag B.Find the prob.that the chess piece drawn from bag B is white.

Condition 1：
1. Drawn a white chess piece from bag A  [ (2/3) ]
2. Drawn a white chess piece from bag B  [ (6+1)/(6+1+8) = (7/15) ]

Condition 2：
1. Drawn a black chess piece from bag A  [ (1/3) ]
2. Drawn a white chess piece from bag B  [ (6)/(6+8+1) = (6/15) ]

The probability
= (2/3)(7/15) + (1/3)(6/15)
= 4/9

probability 2?

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