Question

Leia is operating a digital spinner game in which a player spins an arrow and is given a prize based on where the spinner lands. Leia can program the probability of each of the outcomes. The stuffed teddy bear is the best prize, so she programs the spinner so that the probability of not getting a bear twice in a row is greater than 3  times the probability of getting the teddy bear in one spin. Write an inequality that compares the probability of getting the teddy bear to the probability of not getting the teddy bear, using p  to represent the probability of getting the teddy bear in one try.

Answer 1

In the problem, we are given that the probability of getting a bear is equal to p. Where probability is the ratio of successful outcome (bear) over total outcomes (total number of prizes).

The probability of not getting a bear twice in a row is consisting of 2 attempts:

Attempt 1: 1st spin gets a bear, 2nd spin does not get a bear

total probability of attempt 1 = p * (1 – p)

Attempt 2: 1st spin does not get a bear, 2nd spin gets a bear

total probability of attempt 1 = (1 – p) * p

The overall probability of the 2 attempts is the simply the sum of the 2:

Overall probability of not getting a bear twice in a row= p * (1 – p) + (1 – p) * p

Simplifying:

Overall probability of not getting a bear twice in a row = 2p * (1 – p)

It is stated that the:

probability of not getting a bear twice in a row > 3 times the probability of getting the teddy bear

This is equivalent to:

2p * (1 – p) > 3 p (ANSWER)