Question

According to the general equation for conditional probability, if p (a^b')=1/6 and p(b')=7/12 , what is p(a[b) ?

Answer 1

P(B) = 1 - P(B') = 1 - (7/12) = 5/12
\[\large P(A \cap B)=\frac{P(A \cap B')}{P(B')} \times \frac{P(B)}{1}\]
@Emjay9295 Can you follow so far?

Answer 2

Plugging values into the last equation we get:
\[\large P(A \cap B)=\frac{1\times12\times5}{6\times7\times12}=\frac{5}{42}\]
Now we can make use of the following formula
\[\large P(A|B)=\frac{P(A \cap B)}{P(B)}\]
by plugging in the values that we have found.

Answer 3

yeah i got what you did so far, but how would i use the 5/42? in the formula?

Answer 4

Would it be the top part of the formula?

Answer 5

and the bottom would be 7/12?

Answer 6

That is correct. 5/42 is the numerator and the denominator is 5/12.

Answer 7

so from there how would i go about solving that? Would i be looking to divide those two fractions as is? Or would i switch it to a decimal and divide them?

Answer 8

The bottom (denominator) is P(B) which equals 5/12.
\[\large P(A|B)=\frac{5\times12}{42\times5}=you\ can\ calculate\]

Answer 9

Is 60/210

Answer 10

Do you have a choice of answers? If so, are they fractions or are they decimal numbers?

Answer 11

They are fractions A. 3/7 B .2/7 C.4/7 D.5/7

Answer 12

Which i think it is 2/7 at this point

Answer 13

Yes, the fraction that you calculated simplifies to 2/7.

Answer 14

Thank you for your help, it's really appreciated!

Answer 15

You're welcome :)