A box contains 12 red tokens and 5 green tokens. i. If 4 tokens are selected at

Question

A box contains 12 red tokens and 5 green tokens.

i. If 4 tokens are selected at random, without replacement, determine the probability that at least two of the selected tokens are red.

Probability =

ii. Instead, if 4 tokens are selected at random, with replacement, determine the probability that at least two of the selected tokens are red.

Probability =

iii. Instead, if tokens are selected at random, one at a time and with replacement, determine the probability that the first red token appears on draw 9.

Probability =

Explanation / Answer

i) P(atleast 2 red tokens) = 1 - P(0 red tokens) - P(1 red token) = 1 - [5/17 * 4/16 * 3/15 * 2/14] -
[(12/17 * 5/16 * 4/15 * 3/14) + (5/17 * 12/16 * 4/15 * 3/14) + (5/17 * 4/16 * 12/15 * 3/14) + (5/17 * 4/16 * 3/15 * 12/14)]
= 0.947479

ii) P(atleast 2 red tokens) = 1 - P(0 red tokens) - P(1 red token) = 1 - [5/17]^4 - [4*(12/17)*(5/17)^3] = 0.9206786

iii) P(GGGGGGGGR) = (5/17)^8 * (12/17) = 0.0000395276

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