Let "I" be the event that the first box is chosen, "II" be the event that the second box is chosen, "R" be the event that the red bulb is chosen, and "W" be the event that the white bulb is chosen.
Given that
Construct a probability tree and show all relevant probabilities.
We have that
Then
b. What is the probability of withdrawing a red bulb?
By the Theorem of total probability
"P(R)=0.5(0.3)+0.5(0.1)=0.2"
c. If a red bulb is withdrawn, what is the probability that it came from box 2?
By the Bayes' rule
"P(II \\ | \\ R)={0.5(0.1) \\over 0.5(0.3)+0.5(0.1)}=0.25"
Comments
Dear Aisha. Please use a panel for submitting new questions.
Let X have MGF MX (t) =1/8(1+ e^t ) a) Find E(X) using MX(t) b) Find the variance of X using MX(t). c) Find the moment generating function of Y=2X-1.
If you can't see clearly a picture of the probability tree, then please click on the image of the probability tree, it will open a new web-page. Explanations for the probability tree were written in the text of the solution before the image of the probability tree.
the probability tree not clear
The solution was published.
what is the solution
Leave a comment