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Difficulty: MediumSingle Event Probability

An armory stores a mixture of lithium, alkaline, and nickel-metal hydride (NiMH) batteries. The probability of randomly selecting a lithium battery from the storage is 25\frac{2}{5}. If there are exactly 4848 lithium batteries in the armory, what is the total number of batteries stored?

  1. A
    7272
  2. 120120Answer
  3. C
    168168
  4. D
    240240

Answer

The total number of batteries stored is 120.
The correct answer is found by setting up the proportion derived from the probability definition: 2/5 = 48/x. Cross-multiplying gives 2x = 240, and dividing by 2 results in 120 total batteries.

Step-by-Step Solution

1
Set up the probability formula using the given information.
Probability=Number of LithiumTotal Batteries\text{Probability} = \frac{\text{Number of Lithium}}{\text{Total Batteries}}, so 25=48x\frac{2}{5} = \frac{48}{x}, where xx is the total number of batteries.
Single event probability is the ratio of favorable outcomes to the total number of possible outcomes.
2
Solve the proportion for xx by cross-multiplying.
2x=5×482x = 5 \times 48
Cross-multiplying allows us to solve an equation with fractions and isolate the variable terms.
3
Simplify the equation and isolate xx.
2x=2402x = 240, so x=2402=120x = \frac{240}{2} = 120.
Dividing both sides by 2 isolates the variable, revealing the total number of batteries.

Key Concept

Calculating the total number of outcomes given the probability of a single event and the number of favorable outcomes.
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Topics

Single Event Probability

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