Question

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 \dfrac{9}{4} 4 9 ​ start fraction, 9, divided by, 4, end fraction times the probability of getting "Honey Bunny" in one try. Write an inequality that models the situation. Use ppp to represent the probability of getting "Honey Bunny" in one try.

Answer 1

(1-p)^2>9/4p

Explanation:

Answer 2

`[P(X_(1))* P (X_(2))]>[(9)/(4)* P (H_(1))]`

Explanation:

Let the candy "Honey Bunny" be labelled as H and the other candies as X.

It is provided that 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.

• Probability of getting a candy other than "Honey Bunny" twice in a row,

P (X₁) × P (X₂)

• Probability of getting "Honey Bunny" in one try,

P (H₁)

The inequality is as follows:

`[P(X_(1))* P (X_(2))]>[(9)/(4)* P (H_(1))]`