These quizzes explore games that move into the mathematical realm of conditional probability. Essentially, conditional probability is what you need when you are given additional information that should make you want to update your overall estimates about the probability of the events you care about.

For example, consider these two scenarios:

You flip a coin 5 times. What’s the probability the last two flips are both heads,

**given that the first 3 flips were all heads**?You flip a coin 5 times. What’s the probability the last two flips are both heads,

**given that exactly 4 of the 5 flips were heads**?

The answer to question 1 is \(\frac{1}{4}.\) The fact that the first 3 flips were all heads tells us nothing about what the last 2 flips might be. It’s equally likely that they’re HH, HT, TH, or TT. No conditional probability is required.

In question 2, the additional information tells us more about the coin flips. Since 4 of the 5 flips were heads, it is much more likely that the last two flips were heads. What is the answer to question 2?

Of the green apples, three are poisoned and two are normal. Of the red apples, two are poisoned and three are normal. A total of two poisoned apples is necessary in order to kill you. If you must choose one of the following two options, which gives you a higher chance of survival?

**A.** Eat two green apples (2 out of 5 are normal)

**B.** Eat three red apples (3 out of 5 are normal)

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