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Lisa owns a "Random Candy" vending machine, which is a machine that picks a candy out of an assortment in a random fashion. Lisa controls the probability of picking each candy.
The machine is running out of "Honey Bunny," so Lisa wants to program it so that the probability of getting a candy other than "Honey Bunny" twice in a row is greater than
(9)/(4) times the probability of getting "Honey Bunny" in one try.
Write an inequality that models the situation. Use
p to represent the probability of getting "Honey Bunny" in one try.

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Lisa owns a

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One-step inequalities: word problems

Full solution

Q. Lisa owns a

Define Probability: Let $p$ be the probability of getting ＂Honey Bunny＂ in one try. The probability of not getting ＂Honey Bunny＂ in one try is $1 - p$ .
Calculate Probability of Not Getting Twice: To find the probability of not getting ＂Honey Bunny＂ twice in a row, we multiply the probability of not getting it in one try by itself: \(1 - p) \times ( $1$ - p) = ( $1$ - p)^ $2$ \
Set Up Inequality: Lisa wants this probability to be greater than $(\frac{9}{4})$ times the probability of getting ＂Honey Bunny＂ once, which is $(\frac{9}{4}) \times p$ . So, we set up the inequality: $(1 - p)^2 > (\frac{9}{4}) \times p$ .

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