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Zorluk: KolayCompound Probability

A motor pool dispatcher has a set of 66 vehicle keys on a desk. Exactly 22 of the keys belong to trucks, and 44 belong to sedans. If the dispatcher blindly grabs two keys, one after the other without putting the first back, what is the probability that both keys belong to trucks?

  1. A
    19\frac{1}{9}
  2. B
    215\frac{2}{15}
  3. 115\frac{1}{15}Cevap
  4. D
    311\frac{3}{11}

Cevap

115\frac{1}{15}
The correct answer accurately calculates the compound probability of dependent events. The chance of grabbing a truck key first is 2/6. Because that key is held and not replaced, there is only 1 truck key left among the 5 remaining keys, making the chance of the second draw 1/5. Multiplying these fractions (2/6 × 1/5) results in 2/30, which simplifies to 1/15.

Adım Adım Çözüm

1
Determine the probability of selecting a truck key on the first draw.
26\frac{2}{6}
There are 22 truck keys out of a total of 66 keys.
2
Determine the probability of selecting a truck key on the second draw, assuming one truck key has already been removed.
15\frac{1}{5}
Since one truck key was taken and not replaced, there is now 11 truck key remaining out of a total of 55 keys.
3
Multiply the probabilities of the two dependent events to find the compound probability.
26×15=230=115\frac{2}{6} \times \frac{1}{5} = \frac{2}{30} = \frac{1}{15}
The probability of two dependent events both occurring is the product of their individual probabilities.

Anahtar Kavram

Compound Probability (Dependent Events)
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Konular

Compound Probability

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