1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Understanding Conditional Probabilities

  1. Jun 26, 2012 #1
    1. The problem statement, all variables and given/known data
    Suppose you have 3 nickels and 4 dimes in your right pocket and 2 nickels and a quarter in your left pocket. You pick a pocket at random and from it select a coin at random. If it is a nickel, what is the probability that it came from your right pocket?

    2. The attempt at a solution

    Let N be the event of picking a nickel, and R be the event of picking the right pocket.

    My understanding is as follows:

    What the question is asking for is [itex]P_{N}(R)[/itex], that is, the probability of picking the right pocket, given that you already picked a nickel.

    I understand that
    [itex]P(NR) = P(N)\bullet P_{N}(R)[/itex].

    I figured that [itex]P(NR) = \frac{1}{2}\frac{3}{7}[/itex] because there is a 50% chance I pick the right pocket and then a 3/7th chance that within that pocket I pick a nickel.

    If I am making a mistake I suspect this is it.

    Then I also figured that [itex]P(N)=\frac{5}{10}[/itex] since out of the total 10 coins in both pockets, 5 of them are nickels.

    So I simply solved for [itex]P_{N}(R)[/itex] and I got [itex]\frac{3}{7}[/itex], which is wrong.

    But where is my logic incorrect?
    Last edited: Jun 26, 2012
  2. jcsd
  3. Jun 26, 2012 #2
    P(N) looks wrong, you cannot say that there are 5 total nickels and 10 total coins. Instead, you have to sum the probability of picking a nickel out of the right pocket and picking a nickel out of the left pocket.
  4. Jun 27, 2012 #3


    User Avatar
    Science Advisor

    Yes, you can say "there are 5 total nickels and 10 total coins". That is given. What you cannot do is say "there is a 50% chance I pick the right pocket" when that is the probability you are asked to find.

    You have a total of 5 nickels, three in your left pocket and two in your right. If you take a nickel out of your pockets, the probability it came from your right pocket is 2/5.
  5. Jun 27, 2012 #4
    You're right, what I meant to say was that you cannot use that fact alone to find his P(N), you need to know the distribution in each pocket.

    But the answer I got was 9/23.
    There is a 3/7 chance of picking a nickel out of the right pocket, and a 2/3 chance of picking a nickel out of the left pocket. So the probability of the nickel coming from the right pocket is [itex]\frac{\frac{3}{7}}{\frac{3}{7} + \frac{2}{3}} = \frac{9}{23}[/itex].

    Unless my logic is wrong.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Similar Threads for Understanding Conditional Probabilities Date
Understanding the ratio formula Mar 26, 2018
Help me understand addition of 2 rational fn's Jan 29, 2018
Help understanding quotients Jan 11, 2018
Help me understand what a basis is Nov 12, 2017
Don't understand this conditional probabillity example Apr 17, 2012