Question

For two independent events A and B, P(A or B) = 0.70, P(A) = 0.50, and P(B) = 0.45.

Find P(A and B)

Answer 1

We know that
\[P(A\ or\ B)=P(A)+P(B)-P(A\ and\ B)\]
so
\[P(A\ and\ B)=P(A)+P(B)-P(A\ or\ B)\]
I think you can find now?

Answer 2

so i wuld do 50%+45%-70%??

Answer 3

no

Answer 4

well maybe
if the events are independent, then
\[P(A\cap B)=P(A)\times P(B)\]

Answer 5

so 50% *45%

Answer 6

if they are independent you should get the same answer in either case, so i should not have said "no" but rather should have said you can use either method

Answer 7

so 22.5%

Answer 8

\[.5+.45-.7=.25\] and also
\[.5\times .45=.225\] so in fact since they are not the same answer the events are NOT independent and the question is wrong!!

Answer 9

its not a true or false question

Answer 10

hmmm where did this question come from? it is always true that
\[P(A\cap B)=P(A)+P(B)-P(A\cup B)\] but if the events are independent then it is also true that
\[P(A\cap B)=P(A)\times P(B)\] so there is some mistake here

Answer 11

i copyed and pastened it
so it wasnt my typo

Answer 12

i believe you
is it from a book or a worksheet or what?
if you want, you should alert your teacher to the fact that the events here cannot be independent with the probabilities given

Answer 13

because in this case
\[.5+.45-.7\neq .5\times .45\] so the events are definitely not independent

Answer 14

i dont exactl yhave a techer

Answer 15

where does the question come from?

Answer 16

my online schol

Answer 17

write them and tell them there is a mistake in the question
if they remove the word "independent" then it would be find, use method one and get \(.45-.5-.7=.25\)
but you cannot just claim two events are independent. you have to show that they are

Answer 18

*fine

Answer 19

i suspect that the questions are written without much care, or expertise on the part of the writers. someone just wrote it down without thinking