Sequential or Simultaneous Draw!

Probability Level 2

You have six strips of paper. The word 'YES' is written on three on them. The word 'NO' is written on the other three Then all six are folded in a manner that they are identical.

Mr. A draws in the following manner. All six strips are tossed and Mr. A chooses one of them. The chosen strip is opened and the choice recorded. The strip is then folded again and a second draw is done in the same manner.

Mr. B draws in the following manner. All six strips are tossed and Mr. B chooses two of them. The chosen strips are opened and the choices recorded.

Who has the better chance of drawing two 'YES'es?

Mr. B Both have the same chance Mr. A

2 solutions

L S
Jan 30, 2015

For the first draw, A and B have the same probability of drawing a YES.

Probability of A drawing two YESes is $\frac{3}{6}*\frac{3}{6}=\frac{1}{4}$ .

Probability of B drawing two YESes is $\frac{\binom{3}{2}}{\binom{6}{2}}=\frac{1}{5}$ .

Therefore A has a better chance of drawing two YESes

Math is for all sigma factorial? Grin

Calvin Lin Staff - 6 years, 4 months ago

Edit: Sorry i misread the question. I thought that the strips were drawn 3 times, instead of 2.

I disagree with the probability of drawing two YESes. What you found is the probability that the first strip is a YES, and the second strip is a YES, and the third strip is anything.

Calvin Lin Staff - 6 years, 4 months ago

I think that Mr. Janardhanan Sivaramakrishnan forgot to mention that "Mr. A"

makes two draws only.

Dev Mehra - 6 years, 4 months ago

Did I not write "...and a second draw is done in the same manner." ? OR was that courtesy of the moderators?

Janardhanan Sivaramakrishnan - 6 years, 4 months ago

@Janardhanan Sivaramakrishnan – You are right Mr. Janardhanan Sivaramakrishnan.

I must have misread.

My apologies.

Dev Mehra - 6 years, 4 months ago

Janardhanan Sivaramakrishnan
Feb 1, 2015

Case for Mr A. Since the drawn strip is returned to the lot, the probability of the second draw being a YES is independent of the first one. Hence, probability of 2 YESs = $\frac{3}{6}\frac{3}{6}=\frac{1}{4}$

Case of Mr. B Drawing two strips can be regarded as drawing the second strip without returning the first one to the lot. Hence probability of first YES = $\frac{1}{2}$ Probability of a second YES (subject to first being YES) = $\frac{2}{5}$

Total probability of 2 YES for B = $\frac{1}{2}\frac{2}{5}=\frac{1}{5}$

Hence, Mr A has a better chance.

Sequential or Simultaneous Draw!

2 solutions

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