Phonesmart is having a sale on Bananas. If you buy one Banana at full price, you get a second at half price. When couples come in to buy a pair of phones, sales of Apricots and Bananas are equally likely. Moreover, given that the first phone sold is a Banana, the second phone is twice as likely to be a Banana rather than an Apricot. What is the probability that a couple buys a pair of Bananas?

The probability that a couple buys a pair of Bananas is 1/3 or 33.3%

Step-by-step explanation:

Let's recall that the formula of probability is:

Probability = Number of favorable outcomes/Total number of possible outcomes

What is the probability that a couple buys a pair of Bananas?

For answering this question, we first need to calculate the probability of buying a first Banana, given that when couples come in to buy a pair of phones, sales of Apricots and Bananas are equally likely:

Probability of buying a first Banana = 1/2

Probability of buying a first Apricot = 1/2

Now, we can calculate the probability of buying a second Banana, given that the second phone is twice as likely to be a Banana rather than an Apricot.

Probability of buying a second phone = 1

Probability of buying a second Apricot = x

Probability of buying a second Banana = 2x

Solving for x, we have:

x + 2x = 1

3x = 1

x = 1/3 ⇒ 2x = 2/3

Thus, probability of buying a second Banana = 2/3

Finally,

Probability that a couple buys a pair of Bananas = Probability of buying a first Banana * Probability of buying a second Banana

Replacing with the values we know:

Probability that a couple buys a pair of Bananas = 1/2 * 2/3 = 2/6 = 1/3

1/3 = 33.3%

Probability that a couple buys a pair of Bananas = 1/3 or 33.3%