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On a shelf there are 60 novels and 20 poetry books. What is the probability that Person A chooses a novel and walks away with it and then Person B walks up shortly after and picks another novel?

$2$ ) On a shelf there are $60$ novels and $20$ poetry books. What is the probability that Person A chooses a novel and walks away with it and then Person B walks up shortly after and picks another novel?

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Find probabilities using the addition rule

Full solution

Q.

2

) On a shelf there are

60

novels and

20

poetry books. What is the probability that Person A chooses a novel and walks away with it and then Person B walks up shortly after and picks another novel?

Calculate Probability Person A: First, we need to determine the probability that Person A chooses a novel. There are $60$ novels and $20$ poetry books, making a total of $80$ books on the shelf. The probability that Person A picks a novel is the number of novels divided by the total number of books. $\newline$ Calculation: Probability of Person A choosing a novel = Number of novels / Total number of books = $60 / (60 + 20) = 60 / 80 = 3 / 4$
Calculate Probability Person B: Next, we need to calculate the probability that Person B chooses a novel after Person A has already taken one. Now there are $59$ novels and still $20$ poetry books, so the total number of books is $79$ . The probability that Person B picks a novel is the number of remaining novels divided by the new total number of books. $\newline$ Calculation: Probability of Person B choosing a novel = Number of remaining novels / New total number of books = $\frac{59}{59 + 20}$ = $\frac{59}{79}$
Find Overall Probability: To find the overall probability of both events happening (Person A and Person B both choosing novels), we multiply the probabilities of each event. $\newline$ Calculation: Overall probability = Probability of Person A choosing a novel $\times$ Probability of Person B choosing a novel = $(\frac{3}{4}) \times (\frac{59}{79})$
Perform Final Multiplication: Now we perform the multiplication to find the final probability. $\newline$ Calculation: Overall probability = $(\frac{3}{4}) \times (\frac{59}{79}) = \frac{177}{316}$

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