Use the counting techniques from the last chapter. A bag contains two red marbles, three green...

Use the counting techniques from the last chapter. A bag contains two red marbles, three green ones, one fluorescent pink one, two yellow ones, and three orange ones. Suzan grabs three at random. Find the probability of the indicated event.

She gets all the red ones, given that she gets the fluorescent pink one.

Expert Solution

Total marbles = 2 + 3 + 1 + 2 + 3 = 11

P(all red ones | she gets the fluorescent pink one) = P(all red ones and she gets the fluorescent pink one) / P(all red ones | she gets the fluorescent pink one)

P(all red ones and she gets the fluorescent pink one) = 2C2 * 1C1 / 11C3

P(all red ones | she gets the fluorescent pink one) = 1C1 * 10C2 / 11C3

P(all red ones | she gets the fluorescent pink one) = P(all red ones and she gets the fluorescent pink one) / P(all red ones | she gets the fluorescent pink one)

= (2C2 * 1C1 / 11C3) / (1C1 * 10C2 / 11C3)

= 2C2 / 10C2

= 1/45 or 0.0222

orchestra answered 1 year ago

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