The table shows the children nominated to win the subject prize in Mathematics and the subject prize in English.Mathematics EnglishAlice AliceBen ClaireEmma GabiPaddy SimonThe winner of each subject prize is picked at random.It is possible for Alice to win both prizes.In what percentage of the combinations of prize winners does Alice win at least one prize?
Question
The table shows the children nominated to win the subject prize in Mathematics and the subject prize in English.Mathematics EnglishAlice AliceBen ClaireEmma GabiPaddy SimonThe winner of each subject prize is picked at random.It is possible for Alice to win both prizes.In what percentage of the combinations of prize winners does Alice win at least one prize?
Solution
To solve this problem, we need to calculate the total number of combinations for the prize winners and the number of combinations in which Alice wins at least one prize.
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Total combinations: There are 4 nominees for each subject prize, so the total number of combinations for the prize winners is 4 (for Mathematics) * 4 (for English) = 16 combinations.
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Combinations where Alice wins at least one prize: This can be divided into three scenarios:
a. Alice wins both prizes: There is only 1 combination for this scenario (Alice for Mathematics and Alice for English).
b. Alice wins the Mathematics prize only: There are 3 combinations for this scenario (Alice for Mathematics and each of the other 3 nominees for English).
c. Alice wins the English prize only: Similarly, there are 3 combinations for this scenario (each of the other 3 nominees for Mathematics and Alice for English).
So, the total number of combinations where Alice wins at least one prize is 1 (from scenario a) + 3 (from scenario b) + 3 (from scenario c) = 7 combinations.
- To find the percentage, we divide the number of favorable outcomes by the total number of outcomes and multiply by 100. So, the percentage of combinations where Alice wins at least one prize is (7 / 16) * 100 = 43.75%.
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