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Frank and his brother are at a store shopping for a beanbag chair for their school's library. The store sells beanbag chairs with different fabrics and types of filling. $\newline$ The probability that a beanbag chair is made from suede is $0.6$ , the probability that it is filled with beads is $0.2$ , and the probability that it is made from suede and is filled with beads is $0.1$ . $\newline$ What is the probability that a randomly chosen beanbag chair is made from suede or is filled with beads? $\newline$ 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. Frank and his brother are at a store shopping for a beanbag chair for their school's library. The store sells beanbag chairs with different fabrics and types of filling.

\newline

The probability that a beanbag chair is made from suede is

0.6

, the probability that it is filled with beads is

0.2

, and the probability that it is made from suede and is filled with beads is

0.1

.

\newline

What is the probability that a randomly chosen beanbag chair is made from suede or is filled with beads?

\newline

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

Denote Events: Let's denote the events as follows: $\newline$ A: The beanbag chair is made from suede. $\newline$ B: The beanbag chair is filled with beads. $\newline$ We are given the following probabilities: $\newline$ $P(A) = 0.6$ $\newline$ $P(B) = 0.2$ $\newline$ $P(A \text{ and } B) = 0.1$
Use Addition Rule: We need to find the probability that a randomly chosen beanbag chair is made from suede or is filled with beads. We can use the Addition Rule of Probability: $\newline$ $P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$
Substitute Given Values: Substituting the given values, we get: $P(A \text{ or } B) = 0.6 + 0.2 - 0.1$
Correct Calculation: Solving this, we get: $\newline$ $P(A \text{ or } B) = 0.7$ $\newline$ But wait, I made a mistake in the calculation. It should be: $\newline$ $P(A \text{ or } B) = 0.6 + 0.2 - 0.1 = 0.7$

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