Probability - GED Math

1. What does the fundamental counting principle say?

   If one choice can be made $m$ ways and a second $n$ ways, the two together can be made $m \times n$ ways.

2. In how many different orders can $4$ books be arranged on a shelf?

   $24$. $4! = 4 \times 3 \times 2 \times 1$.

3. When do you count with a permutation instead of a combination?

   When order matters (arrangements, rankings, assigned roles). A combination counts selections where order does not matter.

4. How many different $2$-person committees can be chosen from $4$ people?

   $6$. Order does not matter, so $\frac{4 \times 3}{2 \times 1} = 6$.

5. What is the formula for $P(A \text{ or } B)$?

   $P(A) + P(B) - P(A \text{ and } B)$. If $A$ and $B$ cannot happen together, the last term is $0$.

6. The probability of rain tomorrow is 0.35. What is the probability of no rain?

   0.65. The complement is 1 minus 0.35.

7. How do you find $P(A \text{ and } B)$ for independent events?

   Multiply: $P(A) \times P(B)$. Independent means one outcome does not affect the other.

8. A fair coin is flipped twice. What is the probability of getting two heads?

   $\frac{1}{4}$. The flips are independent: $\frac{1}{2} \times \frac{1}{2}$.

9. What is the probability of rolling a number greater than $4$ on a standard six-sided die?

   $\frac{1}{3}$. Two outcomes ($5$ and $6$) out of six: $\frac{2}{6}$.

10. How many outfits can be made from $3$ shirts and $4$ pairs of pants?

    $12$. Multiply the choices: $3 \times 4$.

11. How do you find the probability of an event when all outcomes are equally likely?

    Divide the number of favorable outcomes by the total number of possible outcomes.

12. What is the probability that an event does NOT happen?

    $1 - P(A)$. An event and its complement have probabilities that sum to $1$.

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