1. You are a member of a class of 18students. A bowl contains 18 chips: 1 blue a

Question

   1. You are a member of a class of 18students. A bowl contains 18 chips: 1 blue and 17 red. Each studentis to take 1 chip from the bowl without replacement. The studentwho draws the blue chip is guaranteed an A for thecourse. (a) if you have a choice of drawing first, fifth, or last,which position would you choose? Jusfify your choice on the basisofprobability. (b) Suppose the bowl contains 2 blue and 16 red chips. Whatposition would you now choose?    2. A drawer contains four black, six brown,and eight olive socks. Two socks are selected at random form thedrawer. (a) Compute the probability that both socks are the samecolor. (b) Compute the probability that both socks are olive ifit is known that they are the same color.    1. You are a member of a class of 18students. A bowl contains 18 chips: 1 blue and 17 red. Each studentis to take 1 chip from the bowl without replacement. The studentwho draws the blue chip is guaranteed an A for thecourse. (a) if you have a choice of drawing first, fifth, or last,which position would you choose? Jusfify your choice on the basisofprobability. (b) Suppose the bowl contains 2 blue and 16 red chips. Whatposition would you now choose?    2. A drawer contains four black, six brown,and eight olive socks. Two socks are selected at random form thedrawer. (a) Compute the probability that both socks are the samecolor. (b) Compute the probability that both socks are olive ifit is known that they are the same color.

Explanation / Answer

1)

a)

P(of getting a blue chip if I draw first) = 1/18

P(of getting a blue chip if I draw fifth ) = P(of all 4 whodraws before me gets red chips )*P(I get blue chip)

= (17/18)*(16/17)*(15/16)*(14/15)*(1/14) = 1/18 .

P(of getting a blue chip if I draw last)= P(all 17 ppl who drawsbefore me gets red chips)*P(I get blue chip)

= (17/18)*(16/17)*……(1/2)*(1/1) = 1/18 (as beforeall denominators and numerators cancel out each other and only 18remains in the denominator.

So I should be indifferent to all.

b)

If you treat the row of 18 as a string of 2 Bs and 16 Rs then .Let us find the probability of getting a blue chip at anyposition.

Without loss of generality we pick a nth position.

Total # of ways of arranging all the chips = # of ways ofselecting 2 positions for Bs in 18 = 18C2

# of ways of arranging the chips such that one blue chip goes tonth position = pick one place for the blue chip ins 17other positions = 17C1

P(of getting blue ) = 17C1/18C2

Which is independent of n . So I should again be indifferent towhich position I want to go.

2)

Given socks are 4 B, 6 Br and 8 O.

So

P(getting two of same colour) = P(getting both Black)+P(gettingboth Brown)+P(getting both Olive)

P (# of ways of picking both black socks) = 4c2/18c2 = 6/153

P(# of ways of picking both brown socks) = 6c2/18c2 = 15/153

P(# of ways of picking both olive socks) = 8c2/18c2 =28/153

P(getting two of same colour) = (4c2+6c2+8c2)/18c2 = 49/153 =32.01%

b)

P(both socks are olive |both socks are of same colour)

= P(both socks of same colour they areolive)/P(both socks are of same colour)

= (= 8c2/18c2)/ (4c2+6c2+8c2)/18c2 = 57.14%

Hope this helps. Feel free to ask for any clarifications

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