Calculating the Probability of a Compound Event
Calculating the probability of a compound event is a Grade 7 statistics skill in Big Ideas Math Advanced 2, Chapter 15: Probability and Statistics. Compound event probability uses the same ratio formula as simple events: P(event) equals number of favorable outcomes divided by total possible outcomes. The total outcomes are often found using the Fundamental Counting Principle or a tree diagram or table.
Key Concepts
Property The probability of a compound event is the ratio of the number of favorable outcomes to the total number of possible outcomes. $$P(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$$.
Examples A coin is flipped and a standard six sided die is rolled. The probability of getting tails and a number greater than 4 is $\frac{2}{12} = \frac{1}{6}$. There are 2 favorable outcomes (Tails, 5; Tails, 6) out of 12 possible outcomes. A spinner has 3 equal sections (Red, Blue, Green) and another spinner has 2 equal sections (1, 2). The probability of landing on Blue and 1 is $\frac{1}{6}$. There is 1 favorable outcome (Blue, 1) out of $3 \times 2 = 6$ possible outcomes.
Explanation Calculating the probability of a compound event follows the same principle as for a simple event. First, determine the total number of possible outcomes, often by using the Fundamental Counting Principle, a tree diagram, or a table. Next, count the number of outcomes that are considered favorable for the event. The probability is the fraction formed by placing the number of favorable outcomes in the numerator and the total number of outcomes in the denominator.
Common Questions
How do you calculate the probability of a compound event?
Count the total number of possible outcomes (using the Fundamental Counting Principle, tree diagram, or table), count the favorable outcomes, then divide: P equals favorable divided by total.
What is an example of a compound event probability?
Flipping a coin and rolling a die has 12 total outcomes. The probability of getting tails and a number greater than 4 is 2 favorable outcomes (tails-5 and tails-6) divided by 12, which equals 1/6.
What tools help find total outcomes for compound events?
The Fundamental Counting Principle (multiply the number of outcomes for each event), tree diagrams (branch for each outcome), and organized tables all help list all possible outcomes systematically.
What textbook covers compound event probability in Grade 7?
Big Ideas Math Advanced 2, Chapter 15: Probability and Statistics covers calculating the probability of compound events.