Back to Exercise: Apply the Addition Rule

Exercises: Apply the Addition Rule for the Probability of A or B

Work through each section in order. For "or" probabilities, decide first
whether the events can both happen: if they can, subtract the overlap
P(A and B); if they cannot, the overlap is 0 and you simply add. Convert
counts to probabilities over a single sample space before applying the rule,
and check that your answer is between 0 and 1. Write interpretations in
complete sentences.

Grade 10·21 problems·~32 min·Common Core Math - HS Statistics and Probability·group·hss-cp-b-7

Work through problems with immediate feedback

Warm-Up: Union, Overlap, and the Right Rule

These problems review the ideas the Addition Rule is built on.

You are asked to find the probability of " $A$ or $B$ ." Which combining rule does the connective "or" point to?

The Addition Rule: add the probabilities, then subtract the overlap.

The Multiplication Rule: multiply the probabilities.

Subtract the smaller probability from the larger.

Divide one probability by the other.

One card is drawn from a standard 52-card deck. Let $K = $ "a king" (4 cards) and $H = $ "a heart" (13 cards). How many cards belong to BOTH events, i.e. the overlap $K$ and $H$ ?

Exactly 1 card (the King of Hearts).

0 cards; a card cannot be a king and a heart at once.

17 cards (4 kings plus 13 hearts).

4 cards (all four kings).

A spinner has 8 equal sections numbered 1 through 8. The event "lands on a multiple of 3" is $\{3, 6\}$ . Write the probability of this event as a fraction in the form (favorable)/(total). What is $P(\text{multiple of }3)$ ?

Fluency Practice: Apply the Rule

Apply the Addition Rule. Decide whether there is an overlap to subtract.

One card is drawn from a standard deck. Let $K = $ "a king" with $P(K) = \frac{4}{52}$ and $H = $ "a heart" with $P(H) = \frac{13}{52}$ . The overlap is $P(K \text{ and } H) = \frac{1}{52}$ . Use the Addition Rule to find $P(K \text{ or } H)$ as a fraction with denominator 52.

A single die is rolled. Let $A = $ "even" $= \{2, 4, 6\}$ and $B = $ "greater than 3" $= \{4, 5, 6\}$ , so $A$ and $B = \{4, 6\}$ . Use the Addition Rule to find $P(A \text{ or } B)$ as a fraction with denominator 6.

Two events satisfy $P(A) = 0.5$ , $P(B) = 0.4$ , and $P(A \text{ and } B) = 0.2$ . Use the Addition Rule to find $P(A \text{ or } B)$ as a decimal.

A single die is rolled. Let $C = $ "rolls a 2" and $D = $ "rolls a 5." A single roll cannot be both, so these events are mutually exclusive and $P(C \text{ and } D) = 0$ . Find $P(C \text{ or } D)$ as a fraction with denominator 6.

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