Question

Probability question.

Answer 1

The probability that a person likes Chess is 0.4.
The probability that a person likes Checkers is 0.8.
The probability that a person likes NEITHER Chess or Checkers is 0.12.

with this given information:

Answer 2

Determine:

(a) The probability that a person likes Chess OR Checkers is?
(b) The probability that a person likes Chess AND Checkers is?

Answer 3

But that is if the events are independent, and do we yet know that?

Answer 4

Yeah, that seems like a good argument.

Answer 5

Then I guess that

P(Chess and Checkers)=0.32

P(Chess OR Checkers)=P(Chess)+P(Checkers)-P(Chess and Checkers)
P(Chess OR Checkers)=0.8+0.4-0.32=0.88

Answer 6

Oh I found that for independent events:

If the occurrence of one event does not affect the probability of the other occurring, then the events are independent.

Answer 7

you should not assume the events are independent...though you can prove they are

Answer 8

Zarkon, how do you prove the events are independent/

Answer 9

\[.12=(1-.4)*(1-.8)\]

Answer 10

In other words, the prob that niether happen is equivalent to the profuct of the complements of both?

Answer 11

\[P(\bar{A}\cap \bar{B})=P(\bar{A})P(\bar{B})\]

Answer 12

yes

Answer 13

then \[\bar{A}\text{ and }\bar{B}\] are independent

then any combination of A and B with or without complements are independent

Answer 14

ok, thanks for helping me out!