A cooler contains 4 cans of lemonade, 3 cans of apple juice, and 5 cans of iced tea. Without looking, Mr. Rackovan selects a can, hands it t

Question

A cooler contains 4 cans of lemonade, 3 cans of apple juice, and 5 cans of iced tea. Without looking, Mr. Rackovan selects a can, hands it to his friend, and then selects another can. What is the probability that he selected 2 cans of iced tea? P (iced tea then iced tea)

Question 1 options:

about 0.174 or 17.4%

about 0.152 or 15.2%

about 0.138 or 13.8%

about 0.833 or 83.3%

0

Answers ( No )

    0
    2021-11-23T20:43:51+00:00

    ANSWER

    The number of lemonade in the can is 4. So we write,

    n(L)=4

    The number of apple in the can is 3. So we write,

    n(A)=3

    The number of iced tea in the can is 5. So we write,

    n(I)=5.

    The total number of drinks in the can,

    n(S)=3+4+5=12.

    Probability of selecting a can of an iced tea,

    P(I)=\frac{n(I)}{n(S)}

    P(I)=\frac{5}{12}

    Since he selected the first one and gave it to his friend, the samples space as well as the number of iced tea will reduce by 1.

    Probability of selecting a can of an iced tea again is,

    P(I)=\frac{4}{11}.

    Therefore probability of selecting 2 cans of an iced tea is

    P(2 \:cans of\: iced \:tea)=\frac{5}{12} \times \frac{4}{11}

    P(2 \:cans of\: iced \:tea)=\frac{20}{132}

    P(2 \:cans of\: iced \:tea)=\frac{5}{33}

    P(2 \:cans of\: iced \:tea)=0.152 \: \:or \:\:15.12%.

    The correct answer is option C

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