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Zorluk: ZorSingle Event Probability

A military supply depot receives a shipment of 400400 uniform jackets. Of these jackets, 25%25\% are size Small, 38\frac{3}{8} are size Medium, and the remaining jackets are divided equally between size Large and size Extra-Large. If a quartermaster randomly selects one jacket from the entire shipment, what is the probability that it is a size Extra-Large jacket?

  1. 316\frac{3}{16}Cevap
  2. B
    313\frac{3}{13}
  3. C
    13\frac{1}{3}
  4. D
    12\frac{1}{2}

Cevap

316\frac{3}{16}
The probability of a single event is the number of favorable outcomes divided by the total number of possible outcomes. First, determine the number of Extra-Large jackets. There are 100100 Small jackets (25%25\% of 400400) and 150150 Medium jackets (38\frac{3}{8} of 400400). This leaves 150150 jackets (400−100−150=150400 - 100 - 150 = 150). Since these remaining jackets are divided equally between Large and Extra-Large, there are exactly 7575 Extra-Large jackets. The probability of randomly selecting an Extra-Large jacket is the number of Extra-Large jackets (7575) over the total number of jackets (400400). Simplifying the fraction 75400\frac{75}{400} by dividing the numerator and denominator by 2525 yields 316\frac{3}{16}.

Adım Adım Çözüm

1
Calculate the number of Small jackets in the shipment.
25%25\% of 400400 is 100100 jackets.
To find the remaining jackets, you first need to determine the exact counts of the known sizes.
2
Calculate the number of Medium jackets in the shipment.
38\frac{3}{8} of 400=3×50=150400 = 3 \times 50 = 150 jackets.
Converting the fraction to an exact count is required to subtract from the total.
3
Determine the number of jackets remaining for the Large and Extra-Large sizes.
400−(100+150)=400−250=150400 - (100 + 150) = 400 - 250 = 150 remaining jackets.
Subtracting the known sizes from the total gives the combined count of the remaining two sizes.
4
Calculate the number of Extra-Large jackets.
150÷2=75150 \div 2 = 75 Extra-Large jackets.
The problem states the remaining jackets are divided equally between the final two sizes.
5
Calculate the probability of selecting an Extra-Large jacket.
Probability =75400= \frac{75}{400}.
Single event probability is the number of favorable outcomes divided by the total number of possible outcomes.
6
Simplify the probability fraction.
75400=316\frac{75}{400} = \frac{3}{16}.
Standardized tests require probability fractions to be in simplest form.

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Single Event Probability
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Single Event Probability

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