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A crate containing 24 bottles of fruit juice is made up of 10 bottles of orange, 8 bottles of Apple and 6 bottles of Lemon. If one bottle is picked at random, what is the probability of getting: a) An apple? b) An orange? c) A lemon?

Mathematics

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Answers

3 parts
a

13\frac{1}{3}

b

512\frac{5}{12}

c

14\frac{1}{4}

Step-by-step solution

9 steps

The total number of bottles in the crate is 24.

  • Number of orange bottles = 10
  • Number of apple bottles = 8
  • Number of lemon bottles = 6

The probability of an event is calculated as:

P(event)=Number of favorable outcomesTotal number of possible outcomesP(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}

Part a· 3 steps

Probability of getting an apple

  1. Identify the number of apple bottles and the total number of bottles.

    Number of apple bottles = 8
    Total bottles = 24

  2. Calculate the probability.

    P(Apple)=824P(\text{Apple}) = \frac{8}{24}

  3. Simplify the fraction.

    P(Apple)=8÷824÷8=13P(\text{Apple}) = \frac{8 \div 8}{24 \div 8} = \frac{1}{3}

    The probability of getting an apple is 13\boxed{\frac{1}{3}}.

Part b

512\frac{5}{12}

Probability of getting an orange

  1. Identify the number of orange bottles and the total number of bottles.

    Number of orange bottles = 10
    Total bottles = 24

  2. Calculate the probability.

    P(Orange)=1024P(\text{Orange}) = \frac{10}{24}

  3. Simplify the fraction.

    P(Orange)=10÷224÷2=512P(\text{Orange}) = \frac{10 \div 2}{24 \div 2} = \frac{5}{12}

    The probability of getting an orange is 512\boxed{\frac{5}{12}}.

Part c

14\frac{1}{4}

Probability of getting a lemon

  1. Identify the number of lemon bottles and the total number of bottles.

    Number of lemon bottles = 6
    Total bottles = 24

  2. Calculate the probability.

    P(Lemon)=624P(\text{Lemon}) = \frac{6}{24}

  3. Simplify the fraction.

    P(Lemon)=6÷624÷6=14P(\text{Lemon}) = \frac{6 \div 6}{24 \div 6} = \frac{1}{4}

    The probability of getting a lemon is 14\boxed{\frac{1}{4}}.

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