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Difficulty: MediumExperimental and Theoretical Probability

A bag contains red, blue, and yellow marbles. The theoretical probability of selecting a red marble at random from the bag is 25\frac{2}{5}. In a probability experiment, a marble is drawn from the bag, its color recorded, and then replaced. This procedure is repeated 250250 times, resulting in a red marble being drawn 115115 times. What is the absolute difference between the observed experimental frequency of red marbles and the theoretical expected frequency?

Answer: 15

Answer

15
The theoretical expected frequency of selecting a red marble over 250250 trials is found by multiplying the total trials by the theoretical probability: 250×25=100250 \times \frac{2}{5} = 100. The experimental frequency observed was 115115. Taking the absolute difference gives ∣115−100∣=15|115 - 100| = 15.

Step-by-Step Solution

1
Calculate the theoretical expected frequency of red marble outcomes.
Theoretical expected frequency = 250×25=100250 \times \frac{2}{5} = 100.
Expected frequency is determined by multiplying the number of trials (N=250N = 250) by the theoretical probability (P=25P = \frac{2}{5}).
2
Find the absolute difference between the observed experimental frequency and the theoretical expected frequency.
∣115−100∣=15|115 - 100| = 15.
The observed experimental frequency is 115115 and the theoretical expected frequency is 100100, so the positive difference is 1515.

Key Concept

Experimental Frequency vs. Theoretical Expected Frequency
Estimated Time:1m 30s
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Topics

Experimental and Theoretical Probability

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