A bag contains colored marbles. The theoretical probability of Jonah drawing 2 blue marbles from the bag with replacement is one fifth. If the experiment is repeated 150 times, what is a reasonable prediction of the number of times he will select 2 blue marbles?

one fifth
5
25
30

Theoretical probability of drawing 2 blue marbles from the bag with replacement is given as \(\frac{1}{5}\).

To find a reasonable prediction of the number of times Jonah will select 2 blue marbles when the experiment is repeated 150 times, we can use the expected value formula:

\[ \text{Expected value} = \text{Probability} \times \text{Number of trials} \]

Here, the probability of drawing 2 blue marbles is \(\frac{1}{5}\) and the number of trials is 150. So, we calculate:

\[ \text{Expected value} = \frac{1}{5} \times 150 \]

\[ \text{Expected value} = 30 \]

Thus, a reasonable prediction of the number of times Jonah will select 2 blue marbles is 30.

Do you want any further details or have any questions?

Here are some additional questions you might consider:
1. How is the theoretical probability of an event calculated?
2. What is the difference between theoretical and experimental probability?
3. How does the concept of expected value apply to real-life situations?
4. How would the prediction change if the probability of drawing 2 blue marbles was different?
5. What would be the prediction if the experiment was repeated 200 times?

Tip: Remember that the expected value gives a theoretical average over many trials, not a guarantee of exact outcomes in practice.

Explore how to predict the number of times Jonah will select 2 blue marbles from a bag with theoretical probability. Use the expected value formula to calculate the prediction based on 150 repeated trials. Understand the concept of probability and its application in predicting outcomes.

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