To solve the problem of predicting how many times a blue candy will be chosen out of 100 draws, we need to understand the concepts of probability and expected value.
Here's a step-by-step solution:
1. Identify the Probability of Drawing a Blue Candy:
The probability of drawing a blue candy is given as [tex]\(\frac{3}{10}\)[/tex]. This means that out of every 10 candies drawn, we expect 3 of them to be blue on average.
2. Determine the Total Number of Draws:
The number of times we will draw a candy is given as 100.
3. Calculate the Expected Number of Blue Candies:
To find the expected number of times we will draw a blue candy, we multiply the total number of draws by the probability of drawing a blue candy. This can be expressed as:
[tex]\[
\text{Expected number of blue candies} = \text{Total draws} \times \text{Probability of blue candy}
\][/tex]
Plugging in the given values:
[tex]\[
\text{Expected number of blue candies} = 100 \times \frac{3}{10}
\][/tex]
4. Perform the Multiplication:
Multiply 100 by [tex]\(\frac{3}{10}\)[/tex]:
[tex]\[
100 \times \frac{3}{10} = 100 \times 0.3 = 30.0
\][/tex]
5. Conclusion:
Therefore, we predict that out of 100 draws, a blue candy will be chosen approximately 30 times.
So, the final answer is 30.
