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Emilio just returned from a spring break volunteer trip. He is shopping for a photo album that will showcase his photos from the trip. The albums range in photo capacity and orientation. $\newline$ The probability that a photo album holds under $200$ photos is $0.7$ , the probability that it is oriented horizontally is $0.3$ , and the probability that it holds under $200$ photos and is oriented horizontally is $0.2$ . $\newline$ What is the probability that a randomly chosen photo album holds under $200$ photos or is oriented horizontally? $\newline$ Write your answer as a whole number, decimal, or simplified fraction.

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Find probabilities using the addition rule

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Q. Emilio just returned from a spring break volunteer trip. He is shopping for a photo album that will showcase his photos from the trip. The albums range in photo capacity and orientation.

\newline

The probability that a photo album holds under

200

photos is

0.7

, the probability that it is oriented horizontally is

0.3

, and the probability that it holds under

200

photos and is oriented horizontally is

0.2

.

\newline

What is the probability that a randomly chosen photo album holds under

200

photos or is oriented horizontally?

\newline

Write your answer as a whole number, decimal, or simplified fraction.

Define Events: Let's call the event where a photo album holds under $200$ photos event $A$ , and the event where an album is oriented horizontally event $B$ . We know that: $P(A) = 0.7$ (probability that an album holds under $200$ photos) $P(B) = 0.3$ (probability that an album is oriented horizontally) $P(A \text{ and } B) = 0.2$ (probability that an album holds under $200$ photos and is oriented horizontally)
Apply Addition Rule: We use the Addition Rule of Probability to find $P(A \text{ or } B)$ : $P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$
Calculate Probability: Now we plug in the values we have: $\newline$ $P(A \text{ or } B) = 0.7 + 0.3 - 0.2$
Final Result: Doing the calculation gives us: $\newline$ $P(A \text{ or } B) = 1.0 - 0.2$ $\newline$ $P(A \text{ or } B) = 0.8$

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