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A bag contains 20 balls numbered 1 to 20. If a ball is picked at random, what is the probability that the number is a prime number?
207тАЛ
208тАЛ
209тАЛ
21тАЛ
208тАЛ
Memorize the prime numbers up to 20 (2, 3, 5, 7, 11, 13, 17, 19) so you can count them in seconds without manual checking.
A bag contains 20 balls numbered from 1 to 20. One ball is picked at random.
P(E)=Total┬аNumber┬аof┬аOutcomesritNumber┬аof┬аFavorable┬аOutcomesтАЛ
Memorize the prime numbers up to 20 (2, 3, 5, 7, 11, 13, 17, 19) so you can count them in seconds without manual checking.
Treating 1 as a prime number, which incorrectly increases the favorable count to 9.
Identify Total Outcomes
The bag contains 20 balls numbered 1 to 20, so the total number of possible outcomes is n(S)=20.
n(S)=20
List the Prime Numbers
A prime number is a whole number greater than 1 whose only divisors are 1 and itself. Between 1 and 20, the prime numbers are 2, 3, 5, 7, 11, 13, 17, and 19.
extPrimes={2,3,5,7,11,13,17,19}
Count Favorable Outcomes
Counting the listed prime numbers gives a total of 8 favorable outcomes, so n(E)=8.
n(E)=8
Calculate the Probability
Applying the classical probability formula, we divide the number of favorable outcomes by the total outcomes to get P(E)=208тАЛ.
P(E)=208тАЛ
B is correct because there are 8 prime numbers between 1 and 20, resulting in a probability of 208тАЛ.
Number theory properties such as primes, composites, and divisibility rules are frequently integrated into probability and permutation-combination questions.