Quick Study Guide
- What is Probability? Probability is a numerical measure of the likelihood that an event will occur. It's always a value between 0 and 1, inclusive.
- Probability Formula: For a simple event, the probability is calculated as:
$P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$
- Range of Probability:
- A probability of $0$ means the event is impossible.
- A probability of $1$ means the event is certain to happen.
- A probability of $0.5$ (or $50\%$) means the event is equally likely to happen or not happen.
- Complementary Events: The complement of an event A (often denoted as $A'$) is the event that A does *not* occur. The sum of the probability of an event and its complement is always 1:
$P(A) + P(A') = 1 \implies P(A') = 1 - P(A)$
- Theoretical Probability: This is what *should* happen based on mathematical calculations and ideal conditions. For example, the theoretical probability of rolling a '4' on a fair six-sided die is $1/6$.
- Experimental Probability: This is what *actually* happens based on conducting trials or experiments. It's calculated as:
$P(\text{Event}) = \frac{\text{Number of times the event occurred}}{\text{Total number of trials}}$
Practice Quiz
1. What is the theoretical probability of rolling an even number on a standard six-sided die?
- $1/6$
- $1/3$
- $2/3$
- $1/2$
2. A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If you pick one marble at random, what is the probability that it is a blue marble?
- $5/10$
- $3/10$
- $2/10$
- $1/10$
3. The probability of it raining tomorrow is $0.35$. What is the probability that it will NOT rain tomorrow?
- $0.35$
- $0.50$
- $0.65$
- $0.70$
4. A coin is flipped 50 times. It lands on heads 28 times. What is the experimental probability of landing on tails?
- $28/50$
- $22/50$
- $1/2$
- $50/28$
5. Which of the following describes an event with a probability of $1$?
- Rolling a 7 on a standard six-sided die.
- Flipping a coin and getting either heads or tails.
- Drawing a red card from a deck of cards that contains only black cards.
- Picking a specific numbered ball from a lottery machine.
6. A spinner has 8 equally sized sectors. 3 sectors are red, 2 are blue, and the rest are yellow. What is the probability of the spinner landing on yellow?
- $3/8$
- $2/8$
- $5/8$
- $3/8$
7. From a standard deck of 52 playing cards, what is the probability of drawing a Queen?
- $1/52$
- $4/52$
- $13/52$
- $26/52$
Click to see Answers
- 1. D (Even numbers on a die are {2, 4, 6}. There are 3 favorable outcomes out of 6 total, so $3/6 = 1/2$.)
- 2. B (Total marbles = $5 + 3 + 2 = 10$. Number of blue marbles = 3. So, $P(\text{Blue}) = 3/10$.)
- 3. C (Using complementary probability: $P(\text{NOT Rain}) = 1 - P(\text{Rain}) = 1 - 0.35 = 0.65$.)
- 4. B (If heads occurred 28 times out of 50 flips, then tails occurred $50 - 28 = 22$ times. So, $P(\text{Tails}) = 22/50$.)
- 5. B (An event with a probability of 1 is certain. Flipping a coin will always result in either heads or tails, covering all possible outcomes.)
- 6. D (Red = 3, Blue = 2. Total sectors = 8. Number of yellow sectors = $8 - (3 + 2) = 8 - 5 = 3$. So, $P(\text{Yellow}) = 3/8$.)
- 7. B (A standard deck of 52 cards has 4 Queens (Queen of Hearts, Diamonds, Clubs, Spades). So, $P(\text{Queen}) = 4/52$.)