L asked in Science & MathematicsMathematics · 4 weeks ago

The percentage of smokers among females is found to be 1%. If 5 females are randomly chosen what's the probability that all are smokers?

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  • 4 weeks ago

    We have to assume the probability of each person being a smoker is independent of the others and always 0.01 for females.

    The probability of the first being a smoker is 0.01

    The probability of the second being a smoker is 0.01

    The probability of the third being a smoker is 0.01

    The probability of the fourth being a smoker is 0.01

    The probability of the fifth being a smoker is 0.01

    The probability of all being smokers:

    0.01 * 0.01 * 0.01 * 0.01 * 0.01

    = 0.0000000001

    Or if done using fractions:

    1/100 * 1/100 * 1/100 * 1/100 * 1/100

    = 1/10,000,000,000

    Answer:

    0.0000000001 (or 1 in 10 billion)

    P.S. The actual rates of smoking among adult females in the U.S. is still about 12%, so the result wouldn't be actually that low in the real world. Globally the rates are about 9% of adult females.

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