Combined Probability Flashcards

All 6 cards in this deck

How do you find the probability of one outcome followed by another from a tree diagram?

e.g. P(train to work late) $=0.13$, P(train home late) $=0.06$; find P(both late)

Multiply the probabilities along the branches.
$0.13\times0.06=0.0078$

What are the steps to find the probability of 'exactly one' from a tree diagram?

e.g. a spinner lands on 2 with probability $\frac{1}{3}$ and is spun twice

1. Multiply along one order: $\frac{1}{3}\times\frac{2}{3}=\frac{2}{9}$
2. Multiply along the other order: $\frac{2}{3}\times\frac{1}{3}=\frac{2}{9}$
3. Add: $\frac{2}{9}+\frac{2}{9}=\frac{4}{9}$

What are the steps to estimate the probability of one result then another from the results of an experiment?

e.g. a drawing pin dropped 150 times landed point up 50 times and point down 100 times; find P(up then down)

1. Estimate each probability using the overall total: $\frac{50}{150}$ and $\frac{100}{150}$
2. Multiply them: $\frac{50}{150}\times\frac{100}{150}=\frac{2}{9}$

True or false? A fair dice is thrown twice, so the probability of getting a 6 on both throws is $\frac{1}{6}+\frac{1}{6}=\frac{2}{6}$.

False.
You multiply, not add: $\frac{1}{6}\times\frac{1}{6}=\frac{1}{36}$.

What assumption are you making when you multiply two probabilities together to find the probability of both events happening?

That the events are independent — the outcome of one does not affect the probability of the other.

True or false? To find the probability of 'the same on both' you multiply along each matching path and then add those results.

True. e.g. P(both heads) $+$ P(both tails).