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Introduction to Probability
Charles M. Grinstead
J. Laurie Snell
Charles M. Grinstead
J. Laurie Snell
Table of Contents
1 Discrete Probability Distributions 2 Continuous Probability Densities
3 Combinatorics
4 Conditional Probability
5 Distributions and Densities
6 Expected Value and Variance
7 Sums of Random Variables
8 Law of Large Numbers
9 Central Limit Theorem
10 Generating Functions
11 Markov Chains
12 Random Walks
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conditional probability based on 2 past events
I have two fair coins in my pocket with tails and heads on either side but I
have another coin which has heads on both sides. I randomly take out a coin
from my pocket and toss it. The result is heads. I toss the coin for a
second time, it is heads again.
Now, if i toss the coin a third time, what is the probability I will get
heads.
Let A be the event a coin with heads and tails on either side is chosen
(i.e. not the coin with heads on both sides).
Let h_1 be the event the first toss is heads
Let h_2 be the event the second toss is heads
Let h_3 be the event the third toss is heads
So i need to find P( h_3 GIVEN (h_1 intersect h_2)). I want to limit the
solution to the theorm of total probability and bayes' theorem or anything
simpler. By the way, I've worked out P(h_2 GIVEN h_1) as 3/4 .
How would I find: P( h_3 GIVEN (h_1 intersect h_2))
Best Regards,
George.