1. Three boys (B1, B2, and B3) and three girls (G1, G2, and G3) line up in a random order

for a photograph.

 

(a) What is the probability that all three girls stand next to each other (e.g., B2-G2-G3-G1-

B1-B3)?

 

(b) What is the probability that the boys and girls alternate (e.g., G2-B3-G3-B1-G1-B2)?

 

2. Definitions of ‘simple random sampling without replacement’ (SRSWOR) and ‘simple

random sampling with replacement’ (SRSWR) are given at the end of this document.

 

(a) 10 cards were drawn WITH REPLACEMENT from a standard deck of cards. What is

the probability that cards of both color (red and black) were selected?

 

(b) 10 cards were drawn WITHOUT REPLACEMENT from a standard deck of cards. What

is the probability that cards of both color (red and black) were selected?

 

3. Two cards were drawn WITHOUT REPLACEMENT from a standard deck of cards. Let

A (resp. B) denote the event that the first card (resp. second card) chosen was a diamond.

 

(a) Find P(B).

 

(b) Show that A and B are not independent events.

 

4. In a town, 40% of the population has HIV. An HIV test for a person that actually has the

disease comes back positive with probability 0.9. If a person does not have the disease,

then the test comes back negative with probability 0.95.

If a person is chosen at random from the town population and his/her test came back

 

positive, then what is the probability that the person actually has HIV?

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