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Difficulty: HardSingle Event Probability

A maintenance kit contains 1212 metric wrenches, 1515 standard wrenches, 99 screwdrivers, and an unknown number of pliers. If the probability of randomly selecting a screwdriver from the entire kit is 16\frac{1}{6}, what is the probability of randomly selecting a standard wrench? Express your answer as a fraction in simplest form.

Answer: 5/18 / \frac{5}{18} / 5 / 18

Answer

5/18
By using the given probability of selecting a screwdriver (1/6) and the known count of screwdrivers (9), we determine that the total number of items in the kit is 54 (because 9 is 1/6 of 54). The probability of randomly selecting a standard wrench is then the number of standard wrenches (15) divided by the total (54). Simplifying the fraction 15/54 by dividing both numbers by 3 yields 5/18.

Step-by-Step Solution

1
Set up an equation to find the total number of items in the kit.
9Total=16\frac{9}{\text{Total}} = \frac{1}{6}
The probability of an event is the number of favorable outcomes divided by the total number of possible outcomes. Here, we know the probability and the exact count of screwdrivers.
2
Solve for the total number of items.
\text{Total} = 9 \times 6 = 54
Cross-multiplying isolates the total variable, revealing there are 54 items in the entire kit.
3
Calculate the probability of selecting a standard wrench.
Probability=1554\text{Probability} = \frac{15}{54}
There are 15 standard wrenches out of the 54 total items calculated.
4
Simplify the fraction.
1554=518\frac{15}{54} = \frac{5}{18}
Both 15 and 54 are divisible by 3. Dividing the numerator and denominator by 3 gives the simplest form.

Key Concept

Calculating probabilities by determining the total sample size from a known probability.
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Topics

Single Event Probability

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