26 customers are eating dinner at a local diner. Of the 26 customers, 20 order coffee, 8 order pie, and 7 order coffee and pie. Using this information, answer each of the following questions.

Let $A$ be the event that a randomly selected customer orders coffee and $B$ be the event that a randomly selected customer orders pie.

What is $P(A)$, the probability that a customer orders coffee?
What is $P(B)$, the probability that a customer orders pie?
What is $P(A$ and $B)$, the probability that a customer orders coffee and pie?

What is $P(A$ or $B)$, the probability that a customer orders coffee or pie?

Question

26 customers are eating dinner at a local diner. Of the 26 customers, 20 order coffee, 8 order pie, and 7 order coffee and pie. Using this information, answer each of the following questions.

Let $A$ be the event that a randomly selected customer orders coffee and $B$ be the event that a randomly selected customer orders pie.

What is $P(A)$, the probability that a customer orders coffee?
What is $P(B)$, the probability that a customer orders pie?
What is $P(A$ and $B)$, the probability that a customer orders coffee and pie?

What is $P(A$ or $B)$, the probability that a customer orders coffee or pie?

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Calculate $P(A)$, the probability of a customer ordering coffee. ‖ ‖ step 2 ⋮ From the asksia-ll calculation list, $P(A) = \frac{20}{26}$. Simplify the fraction to its irreducible form. ‖ ‖ step 3 ⋮ Simplifying $\frac{20}{26}$ gives $P(A) = \frac{10}{13}$. ‖ ‖ step 4 ⋮ Convert the probability to a percentage: $P(A) = 76.92\%$. ‖ ∻[question 1] Answer∻ ⚹ $P(A) = \frac{10}{13}$ or $76.92\%$ ⚹ ∻Key Concept∻ ⚹Probability of a single event⚹ ∻Explanation∻ ⚹The probability of an event is the number of favorable outcomes divided by the total number of possible outcomes.⚹ ‖ step 1 ⋮ Calculate $P(B)$, the probability of a customer ordering pie. ‖ ‖ step 2 ⋮ From the asksia-ll calculation list, $P(B) = \frac{8}{26}$. Simplify the fraction to its irreducible form. ‖ ‖ step 3 ⋮ Simplifying $\frac{8}{26}$ gives $P(B) = \frac{4}{13}$. ‖ ‖ step 4 ⋮ Convert the probability to a percentage: $P(B) = 30.77\%$. ‖ ∻[question 2] Answer∻ ⚹ $P(B) = \frac{4}{13}$ or $30.77\%$ ⚹ ∻Key Concept∻ ⚹Probability of a single event⚹ ∻Explanation∻ ⚹The probability of an event is the number of favorable outcomes divided by the total number of possible outcomes.⚹ ‖ step 1 ⋮ Calculate $P(A$ and $B)$, the probability of a customer ordering both coffee and pie. ‖ ‖ step 2 ⋮ From the asksia-ll calculation list, $P(A$ and $B) = \frac{7}{26}$. This fraction is already in its simplest form. ‖ ‖ step 3 ⋮ The probability is given directly: $P(A$ and $B) = \frac{7}{26}$. ‖ ∻[question 3] Answer∻ ⚹ $P(A$ and $B) = \frac{7}{26}$ ⚹ ∻Key Concept∻ ⚹Probability of the intersection of two events⚹ ∻Explanation∻ ⚹The probability of the intersection of two events is the number of outcomes where both events occur divided by the total number of possible outcomes.⚹ ‖ step 1 ⋮ Calculate $P(A$ or $B)$, the probability of a customer ordering coffee or pie. ‖ ‖ step 2 ⋮ Use the formula $P(A$ or $B) = P(A) + P(B) - P(A$ and $B)$. ‖ ‖ step 3 ⋮ Substitute the known probabilities into the formula: $P(A$ or $B) = \frac{10}{13} + \frac{4}{13} - \frac{7}{26}$. ‖ ‖ step 4 ⋮ Find a common denominator and simplify the expression. ‖ ‖ step 5 ⋮ Simplifying gives $P(A$ or $B) = \frac{20}{26} + \frac{8}{26} - \frac{7}{26} = \frac{21}{26}$. ‖ ∻[question 4] Answer∻ ⚹ $P(A$ or $B) = \frac{21}{26}$ ⚹ ∻Key Concept∻ ⚹Probability of the union of two events⚹ ∻Explanation∻ ⚹The probability of the union of two events is found by adding the probabilities of each event and subtracting the probability of their intersection.⚹◊What is the formula for calculating $P(A$ or $B)$, the probability that a customer orders coffee or pie?⍭ Generate me a similar question◊

Sia