Question

what is the probability of drawing two yellow chips(of any numbers) when drawing two chips and...

what is the probability of drawing two yellow chips(of any numbers) when drawing two chips and not replacing the first chip drawn? With replacing?

yellow chips 1,2,3
red chips 1,2,3,4
blue chips 1,2,3,4,5
Math   Statistics-And-Probability   
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Answer #1

There are 3 yellow chips , 4 red chips and 5 blue chips

Total number of chips = 12

  • CASE I : chips are drawn WITHOUT REPLACEMENT procedure

Probability of drawing a yellow chip in the 1st draw = 3C1 / 12C1 = 3/12 = 1/4 = 0.25

Probability of drawing a yellow chip in the 2nd draw = 2C1 / 11C1 = 2/11

Total probability of drawing two yellow chips = 0.25 x (2/11) = 0.0455

  • CASE II : chips are drawn WITH REPLACEMENT procedure

Probability of drawing a yellow chip in the 1st draw = 3C1 / 12C1 = 3/12 = 1/4 = 0.25

Probability of drawing a yellow chip in the 2nd draw = 3C1 / 12C1 = 3/12 = 1/4 = 0.25 (Since , the chip is replaced)

Total probability of drawing two yellow chips = 0.25 x 0.25 = 0.0625

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