05. Learning Objectives - Conditional Probability

Learning Objectives - Conditional Probability

We use the notation where

  • P(A) means "the probability of A"
  • P(\neg A) means "the probability of NOT A"
  • P(A,B) means "the probability of A and B" and
  • P(A|B) means "the probability of A given B.

If A and B are independent events and P(A) = 0.2 and P(B) = 0.1, what is P(A,B)?
SOLUTION: 0.02

If A and B are NOT independent events, and P(A) = 0.2 and P(B) = 0.1, what is P(A, B)?
SOLUTION: Not enough information to answer

If A and B are NOT independent events, and P(A) = 0.2, P(B) = 0.1, and P(B|A) = 0.3 what is P(A|B)?
SOLUTION: 0.6

Note:

The remaining questions deal with two coins.

Coin 1 is fair. When flipped it has a probability of 0.5 for heads and 0.5 for tails.

Coin 2 is biased. When flipped it has a probability of 0.9 for heads and 0.1 for tails.

You grab one of these two coins at random (equally likely that you grabbed coin 1 or 2) and you flip it. What's the probability it comes up heads?
SOLUTION: 0.7

You grab a coin at random and flip it twice.

What's the probability that it comes up tails both times?
SOLUTION: 0.13

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