A box contains 9 vitamin tablets and 5 sugar tablets. Suppose 3 tablets are rand

ID: 3276362 • Letter: A

Question

A box contains 9 vitamin tablets and 5 sugar tablets. Suppose 3 tablets are randomly selected from the box.

What is the probability that all three tablets are sugar tablets? Enter your answer in blank #1.

What is the probability that exactly two of the tablets are vitamin tablets? Enter your answer in blank #2.

What is the probability that at least one of the tablets is a vitamin tablet? Enter your answer in blank #3.

What is the probability that at most one of the tablets is a sugar tablet? Enter your answer in blank #4.

(Round your answers to 4 decimal places and enter your answers as 0.1234 and not as .1234.)

a) P(all three are sugar tablets) = 5C3 / 14C3 = 10 / 364 = 0.0275

b) P(exactly two of the tablets are vitamin tablets) = 9C2 * 5C1 / 14C3 = 36 * 5 / 364 = 0.4945

c) P(at least one of the tablet is a vitamin tablet) = 1 - P(none of the tablets are vitamin tablet)

= 1 - P(all three are sugar tablets)

= 1 - 0.0275

= 0.9725

d) P(at most one of the tablet is sugar tablet) = P(all are vitamin tablets) + P(exactly one is sugar tablet)

= 9C3/14C3 + 5C1 * 9C2 / 14C3

= 84/364 + 5*36/364

= 0.7253

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