1 Six balls are drawn with replacement from an urn with 10 r

1. Six balls are drawn, with replacement, from an urn with 10 red and 11 blue balls. An example outcome is BRBBRR. Find the following probabilities. You may leave your answers in combinatorial form.

(a) P(RBBRRB)

(b) Exactly three red balls are drawn.

2. A fair die is rolled. What is the probability that the roll is a two given that the roll is less than five?

Solution

a)

P(RBBRRB) = (10/21)*(11/20)*(10/19)*(9/18)*(8/17)*(9/16) = 0.01824414 [answer]

b)

There are 21C6 ways to draw any 6 balls.

Meanwhile, there are (10C3)(11C3) to draw 3 red and 3 blue.

Thus,

P = [(10C3)(11C3)]/(21C6) = 0.364882795 [ANSWER]

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