A motor pool dispatcher has a set of 6 vehicle keys on a desk. Exactly 2 of the keys belon… — Armed Services Vocational Aptitude Battery (ASVAB)

A motor pool dispatcher has a set of $6$ vehicle keys on a desk. Exactly $2$ of the keys belong to trucks, and $4$ 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?

A
$\frac{1}{9}$
B
$\frac{2}{15}$
$\frac{1}{15}$ Answer
D
$\frac{3}{11}$

Answer

\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.

Step-by-Step Solution

Determine the probability of selecting a truck key on the first draw.

\frac{2}{6}

There are

2

truck keys out of a total of

6

keys.

Determine the probability of selecting a truck key on the second draw, assuming one truck key has already been removed.

\frac{1}{5}

Since one truck key was taken and not replaced, there is now

1

truck key remaining out of a total of

5

keys.

Multiply the probabilities of the two dependent events to find the compound probability.

\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.

Key Concept

Compound Probability (Dependent Events)

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic