Question

What is mutually exclusive events, independent events and The multiplication theory of probability ?

Answer 1

@kc_kennylau please help....

Answer 2

to events \(A\) and \(B\) are "mutually exclusive" if \(A\cap B=\emptyset\)

Answer 3

it means they cannot happen at the same time
like if you roll two dice the total can't be even and 7

Answer 4

two events \(A\) and \(B\) are "independent" means
\[P(A|B)=P(A)\]

Answer 5

Two events are mutually exclusive if they can't have the same outcome. Two events are independent when the probability of one doesn't affect the outcome of the other.

Answer 6

in other words, knowing that \(B\) has occurred gives no additional information about the probability of \(A\)
for example, if you flip a coin twice and know the first toss is heads, it does not change the probability of the second toss being heads

Answer 7

"multiplication" will be
\[P(A\cap B)=P(A)\times P(B|A)\]

Answer 8

if \(A\) and \(B\) are independent, this means
\[P(A\cap B)=P(A)\times P(B)\]

Answer 9

since if \(A\) and \(B\) are independent, then \(P(B|A)=P(B)\)

Answer 10

Since in mutually exclusive events both cannot occur at the same time we add it right ?

In independent events since both are independent or one doesn't affect the other we multiply it... Am i correct ?