1. A box contains two blue marbles and three yellow marbles. (a) Five draws are

Question

1. A box contains two blue marbles and three yellow marbles.

(a) Five draws are made at random with replacement.

i. Find the chance of getting exactly two blue marbles.

ii. Find the chance of getting at least one blue marble.

iii. Are getting a blue marble on the first draw and getting a blue marble on the second draw: independent? Mutually exclusive?

(b) If two draws were made without replacement, would getting a blue marble on the first draw and getting a blue marble on the second draw be: independent? Mutually exclusive?

Explanation / Answer

1) P(drawing one blue marble) = 2/5 = 0.4

n = 5

a) i) P(X = 2) = 5C2 * (0.4)^2 * (0.6)^3 = 0.3456

ii) P(X > 1) = 1 - P(X < 1)

= 1 - P(X = 0)

= 1 - (5C0 * (0.4)^0 * (0.6)^5)

= 1 - 0.078 = 0.922

iii) independent

B) dependent

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