Mathematics
A square dartboard has sections numbered from 1 to 12 as shown below. Players have to make a prediction and throw a dart. They win if their dart lands on the section that matches their prediction. Three friends Amit, Aryan and Aman took the challenge.
Based on the above information, answer the following :
(i) What is the probability of Amit winning if he predicted that his dart will land on a prime number ?
(ii) What is the probability of Aryan winning if he predicted that his dart will land on an odd number ?
(iii) What is the probability of Aman winning if he predicted that his dart will land on a square number ?
(iv) Which of the three friends has the highest chance of winning ?
Probability
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Answer
The dartboard has 12 equally likely sections numbered 1 to 12, so the total number of outcomes = 12.
By formula,
Probability of an event =
(i) Prime numbers from 1 to 12 are 2, 3, 5, 7 and 11, i.e. 5 numbers.
∴ P(Amit wins) = .
Hence, the probability of Amit winning = .
(ii) Odd numbers from 1 to 12 are 1, 3, 5, 7, 9 and 11, i.e. 6 numbers.
∴ P(Aryan wins) = .
Hence, the probability of Aryan winning = .
(iii) Square numbers from 1 to 12 are 1, 4 and 9, i.e. 3 numbers.
∴ P(Aman wins) = .
Hence, the probability of Aman winning = .
(iv) Comparing the three probabilities :
Since is the largest, Aryan has the highest chance of winning.
Hence, Aryan has the highest chance of winning.
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