How do you combine probabilities?

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How do you combine probabilities?

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Answer 1 · 2017-02-16T07:55:16

This is quite a complex question, but here is a short explanation.

Let's us a pack of cards as an example. Single event probabilities involve only ONE aspect.

$P (Heart) = \frac{13}{52} = \frac{1}{4}$ $P("Heart") = 13/52 = 1/4$

$P (Jack) = \frac{4}{52} = \frac{1}{13}$ $P("Jack") = 4/52 = 1/13$

If we combine probabilities, we are considering two or more aspects.
If we ask, "What is the probability that a card is a Heart OR a jack, we are widening the options. "OR" implies ADD.

$P (H or J) = P (H) + P (J) - P (H J)$ $P(H " or " J) = P(H) + P(J) - P(HJ)$

$= \frac{13}{52} + \frac{4}{52} - \frac{1}{52} = \frac{16}{52} = \frac{4}{13}$ $= 13/52 +4/52 - 1/52 = 16/52 = 4/13$

Note that we subtract the combination that is the Heart and the Jack, because that card has been counted twice.

If we ask, "What is the probability that a card is a Heart AND a jack, we are narrowing the options because we are being more specific. "AND" implies MULTIPLY.

$P (H and J) = P (H) \times P (J)$ $P(H " and " J) = P(H) xx P(J)$

$= \frac{13}{52} \times \frac{4}{52} = \frac{1}{52}$ $=13/52 xx4/52 = 1/52$

The answer makes sense, because there is only one card that is a Heart and a Jack.

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How do you combine probabilities?

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