Question

Use Bayes' theorem or a tree diagram to calculate the indicated probability. Round your answer to four decimal places.
Y1, Y2, Y3 form a partition of S. P(X | Y1) = .1, P(X | Y2) = .8, P(X | Y3) = .1, P(Y1) = .3, P(Y2) = .2.

Find P(Y1 | X).

Answer 1

P(Y1 | X ) = P(Y1 AND X) / P(X)

Answer 2

find them and plugin

Answer 3

P(Y1 AND X) = P(Y1) * P(X | Y1)
= 0.3 * 0.1

Answer 4

any idea how to find P(X) ?

Answer 5

would it be .1?

Answer 6

P(X) = P(X| Y1) * P(Y1) + P(X | Y2) * P(Y2) + P(X | Y3) * P(Y3)

Answer 7

P(X) = 0.1 * 0.3 + 0.8 * 0.2 + 0.1 * 0.5

Answer 8

simplify

Answer 9

.24?

Answer 10

yes, thats the probability for P(X)
plugit in the formula

Answer 11

if we had worked this using tree diagams, things wud have been bit clear ...

Answer 12

finish the problem first,
then we can try to visualize it using tree diagram maybe /

Answer 13

sweet i got it! (.3*.1)/.24 = .125

Answer 14

thats correct !
lets draw tree diagram now

Answer 15

Y1, Y2, Y3 form a partition of S

Answer 16

since the probability must equal 1,
P(Y3) must equal 0.5

Answer 17

^^

Answer 18

fine, so far ?