Question

Please help check my answers!

Let E and F be events such that P(E)=0.45 and P(F)=0.17. Find:

a. P(E^c) -> I got 0.55
b. P(not F) -> I got 0.38
c. P(E or F) assuming E and F are mutually exclusive -> I got 0.62
d. P(E) or (F) assuming independent -> I got 61.9235

Answer 1

P(not F) should be 0.83 since

P(not F) + P(F) = 1

P(not F) = 1 - P(F)

P(not F) = 1 - 0.17

P(not F) = 0.83

Answer 2

A and C are correct

Answer 3

D looks a bit odd. I don't know what to make of it

Answer 4

Thank you. For D I did P(E) + P(F) - P(E and F)

Answer 5

so they want to know P(E or F) for part D?

Answer 6

Yes, sorry, typed it wrong

Answer 7

If so, then,

P(E or F) = P(E) + P(F) - P(E and F)

P(E or F) = P(E) + P(F) - P(E)*P(F)

P(E or F) = 0.45 + 0.17 - 0.45*0.17

P(E or F) = 0.5435

Answer 8

P(E and F) = P(E)*P(F) only because E and F are assumed to be independent events

Answer 9

thanks for your help!

Answer 10

np

Answer 11

d. P(E) or (F) assuming independent -> \[=P(E | \neg F)+P(F)\]

Answer 12

=.83*.45+.17=.5435

nvm

Answer 13

a. P(E^c) sorry, could someone explain what E^c means ... what's c?

Answer 14

the ^c means complement

a complement of a set or event is simply everything but that set or event

http://en.wikipedia.org/wiki/Complement_%28set_theory%29

Answer 15

So for example

R = event that it rains

that means R^c = even that it does not rain

Answer 16

thanks :)