Math Problem Statement
Krysta brought 30 bagels to school, 22 of which are poppy seed and 7 of which are blueberry.
If Krysta randomly gives away 4 bagels to teachers, what is the probability that 2 of the chosen bagels are poppy seed and 2 are blueberry?
Write your answer as a decimal rounded to four decimal places.
Solution
To find the probability that Krysta randomly gives away 4 bagels with exactly 2 being poppy seed and 2 being blueberry, we'll use combinations to determine the number of ways to select the desired bagels and then divide by the total number of ways to choose 4 bagels from the 30.
Step 1: Total ways to select 4 bagels from 30
The total number of ways to select 4 bagels out of 30 is given by the combination formula:
where and :
Step 2: Ways to select 2 poppy seed and 2 blueberry bagels
Next, we find the number of ways to select 2 poppy seed bagels out of the 22 available:
And the number of ways to select 2 blueberry bagels out of the 7 available:
Step 3: Multiply the combinations for poppy seed and blueberry
To find the total number of ways to select 2 poppy seed and 2 blueberry bagels, we multiply the results from Step 2:
Step 4: Probability calculation
Finally, the probability is given by:
Now, let's calculate these values step by step:
- Multiply the combinations for poppy seed and blueberry
- Compute the probability.
Let's compute this:The probability that Krysta randomly gives away 4 bagels with exactly 2 being poppy seed and 2 being blueberry is 0.1770, rounded to four decimal places.
Would you like further details or have any other questions? Here are some related questions:
- How do you calculate combinations in probability problems?
- What is the probability of selecting all 4 bagels as poppy seed?
- How does the probability change if the numbers of bagels change?
- What is the probability of selecting exactly 3 poppy seed bagels?
- How would the probability change if Krysta gave away 5 bagels instead of 4?
Tip: When calculating probabilities involving selections, remember to use combinations (not permutations) as the order of selection does not matter in these cases.
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Math Problem Analysis
Mathematical Concepts
Probability
Combinatorics
Formulas
Combinations formula
Theorems
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Suitable Grade Level
High School
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