1) Suppose that an experiment consists of flipping a coin three times

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1) Suppose that an experiment consists of flipping a coin three times.  The event A is defined as "at least two tails turn up", and the event B is defined as "at least two heads turn up."

a) Compute P(A)

b) Compute P(B)

c) Compute P(A ∪ B)

d) Compute P(A ∩ B)

e) Compute P(AC)

f) Compute P(BC)

g) Compute P(A|B)

h) Compute P(B|A)

i) Are A and B mutually exclusive events?  Why or why not?

j) Are A and B independent events?  Why or why not?

k) Are A and B complements? Why or why not?

2) Following is a joint probability table for coffees produced by Starbucks:

Sumatra (S) Ivory Coast (I) Kenya (K) TOTAL

Decaffeinated (D) 0.28 0.05 0.12 0.45

Regular (R) 0.13 0.13 0.29 0.55

TOTAL 0.41 0.18 0.41 1.00

Use this information to determine the following probabilities:

a) P(S ∩ D)

b) P(R ∩ K)

c) P(R ∩ I)

d) P(S)

e) P(R)

f) P(DC)

g) P(S ∪ I)

h) P(I ∪ K)

i) P(D | S)

j) P(I | R)

k) P(K | R)