Questions: A cooler contains 100 ice cream bars. There are 30 Vanilla bars, 40 Mint Chocolate Chip bars, 10 Chocolate bars, and 20 Rocky Road bars. If one bar is selected at random from the cooler, determine the probability that the bar selected is Rocky Road, Chocolate, or Mint Chocolate Chip.

A cooler contains 100 ice cream bars. There are 30 Vanilla bars, 40 Mint Chocolate Chip bars, 10 Chocolate bars, and 20 Rocky Road bars. If one bar is selected at random from the cooler, determine the probability that the bar selected is Rocky Road, Chocolate, or Mint Chocolate Chip.
Transcript text: A cooler contains 100 ice cream bars. There are 30 Vanilla bars, 40 Mint Chocolate Chip bars, 10 Chocolate bars, and 20 Rocky Road bars. If one bar is selected at random from the cooler, determine the probability that the bar selected is Rocky Road, Chocolate, or Mint Chocolate Chip.
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Solution

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Solution Steps

To determine the probability that the bar selected is Rocky Road, Chocolate, or Mint Chocolate Chip, we need to find the total number of these specific bars and divide it by the total number of bars in the cooler.

  1. Calculate the total number of Rocky Road, Chocolate, and Mint Chocolate Chip bars.
  2. Divide this total by the total number of ice cream bars in the cooler.
Step 1: Total Number of Bars

The cooler contains a total of \( 100 \) ice cream bars.

Step 2: Count of Specific Bars

The counts of the specific types of bars are as follows:

  • Rocky Road bars: \( 20 \)
  • Chocolate bars: \( 10 \)
  • Mint Chocolate Chip bars: \( 40 \)
Step 3: Calculate Desired Bars

The total number of bars that are either Rocky Road, Chocolate, or Mint Chocolate Chip is calculated as: \[ \text{Desired Bars} = 20 + 10 + 40 = 70 \]

Step 4: Calculate Probability

The probability \( P \) that a randomly selected bar is Rocky Road, Chocolate, or Mint Chocolate Chip is given by: \[ P = \frac{\text{Desired Bars}}{\text{Total Bars}} = \frac{70}{100} = 0.7 \]

Step 5: Express Probability as a Fraction

The probability can also be expressed as a simplified fraction: \[ P = \frac{7}{10} \]

Final Answer

The probability that the bar selected is Rocky Road, Chocolate, or Mint Chocolate Chip is \\(\boxed{\frac{7}{10}}\\).

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