URGENT STATISTICS QUESTION, 10 POINTS FOR BEST ANSWER

7. The probability that a band plays Heavy Metal is .35. The probability that a band is Swedish is .10. The probability that a band is both is .04.
a. What is the probability that a band is Swedish or plays Heavy Metal?
b. Given that a band is Swedish, what is the probability they play Heavy Metal?
c. Are being Swedish and playing Heavy Metal independent events?
d. Are being Swedish and playing Heavy Metal awesome events?

P(H) = 0.35
P(S) = 0.10
P(H ∩ S) = 0.04

a.
P(H ∪ S) = P(H) + P(S) - P(H ∩ S)
P(H ∪ S) = 0.35 + 0.1 - 0.04
P(H ∪ S) =0.41
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b.
P(H | S) = P(H ∩ S) / P(S)
P(H | S) = 0.04/ 0.10 = 0.4
P(H | S) = 0.4
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c.
No.

d.
yes