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18 January, 03:46

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?

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  1. 18 January, 06:02
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    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%
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