If a cube is picked 300 times, how many pink cubes do we expect to pick?
Understand the Problem
The question is asking how many pink cubes we expect to pick if a cube is selected 300 times, using the probability given for picking pink cubes.
Answer
The expected number of pink cubes is \( 40 \).
Answer for screen readers
The expected number of pink cubes picked is ( 40 ).
Steps to Solve
- Identify the Probability of Picking Pink Cubes
From the table, the probability of picking a pink cube is given as ( P(\text{pink}) = \frac{2}{15} ).
- Calculate Expected Number of Pink Cubes
To find the expected number of pink cubes when a cube is picked 300 times, we multiply the probability by the total number of picks.
$$ \text{Expected pink cubes} = P(\text{pink}) \times \text{Total picks} $$
Substituting the values:
$$ \text{Expected pink cubes} = \frac{2}{15} \times 300 $$
- Perform the Multiplication
Now, we calculate ( \frac{2}{15} \times 300 ).
First, multiply 300 by 2:
$$ 300 \times 2 = 600 $$
Next, divide 600 by 15:
$$ \frac{600}{15} = 40 $$
The expected number of pink cubes picked is ( 40 ).
More Information
The expected value gives us a prediction of how many pink cubes you would get if you repeated the experiment many times. Using probabilities in this way can help make informed estimations in various situations.
Tips
- Confusing the probability with the number of cubes.
- Forgetting to use both the probability and the total number of picks during calculations.
- Not simplifying fractions correctly during multiplication or division.
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