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# Conditional Probability - Problem 1

###### Carl Horowitz

###### Carl Horowitz

**University of Michigan**

Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

A frequent application of conditional probability is where we are given a bunch of just information, so in this case what we're looking at is probability of a and b is 1/4 probability of b given a is 2/3 and we are asked to find the probability of a.

For something like this, all we have to do is plug it into our relationship. We have a formula for conditional probability, all we need to do is plug in the data and solve for the thing we're looking for.

So probability of b given a is 2/3 is equal to probability of a and b 1/4 divided by probability of a, solve this out all we have to do is multiply both sides by probability of a so we end up with 2/3 probability of a is equal to 1/4, multiply both sides by 3/2 and we end up with the probability of a is equal to that's a 3/2 isn't it? 3/2 probability of a is equal to 3 over 8.

So a simple application of conditional probability, take what they give you, plug into the formula and solve accordingly.

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###### Carl Horowitz

B.S. in Mathematics University of Michigan

He knows how to make difficult math concepts easy for everyone to understand. He speaks at a steady pace and his step-by-step explanations are easy to follow.

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