Combined Probabilities Flashcards

All 6 cards in this deck

What is the multiplication rule for two independent events?

e.g. $P(\text{Owen scores})=0.4$, $P(\text{Wasim scores})=0.25$

$P(A \text{ and } B) = P(A) \times P(B)$

e.g. $P(\text{both score}) = 0.4 \times 0.25 = 0.1$

What is the addition rule for mutually exclusive events?

e.g. $P(\text{win})=0.3$, $P(\text{draw})=0.1$ in one game

$P(A \text{ or } B) = P(A) + P(B)$

e.g. $P(\text{win or draw}) = 0.3 + 0.1 = 0.4$

True or false? If $P(\text{Owen scores}) = 0.4$ and $P(\text{Wasim scores}) = 0.25$, then the probability that both score is $0.4 + 0.25$.

False. For 'both', independent probabilities should be multiplied: $0.4 \times 0.25$.

True or false? $P(A \text{ or } B) = P(A) + P(B)$ for any two events $A$ and $B$.

False. Adding only works for mutually exclusive events; otherwise an outcome could be in both categories and gets counted twice.

How do you find the probability of 'at least one' of several events happening?

e.g. two tests, $P(\text{fails both}) = 0.0351$

$1 - P(\text{none of them happen})$

e.g. $P(\text{passes at least one}) = 1 - 0.0351 = 0.9649$

What are the steps to find the probability that exactly one of two independent events happens?

e.g. $P(A)=0.3$, $P(B)=0.5$

1. $P(A \text{ and not } B) = 0.3 \times 0.5 = 0.15$
2. $P(\text{not } A \text{ and } B) = 0.7 \times 0.5 = 0.35$
3. Add the two: $0.15 + 0.35 = 0.5$