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A box contains 50 tickets numbered 1 to 50. One ticket is drawn at random. What is the probability that the number on the ticket is a multiple of 5 or 10?
51тАЛ
101тАЛ
21тАЛ
41тАЛ
51тАЛ
Recognize that all multiples of 10 are already multiples of 5, so the condition 'multiple of 5 or 10' simplifies directly to finding the multiples of 5.
Total tickets = 50, numbered from 1 to 50
P(E)=Total┬аOutcomesFavorable┬аOutcomesтАЛ
Recognize that all multiples of 10 are already multiples of 5, so the condition 'multiple of 5 or 10' simplifies directly to finding the multiples of 5.
Double counting the multiples of 10 by adding the counts of both sets separately without accounting for their complete overlap.
Identify total outcomes
Since the tickets are numbered from 1 to 50, the total number of possible outcomes is 50.
N=50
Determine favorable outcomes
The numbers between 1 and 50 that are multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50. Since every multiple of 10 is also a multiple of 5, the total number of favorable outcomes is 10.
n(E)=10
Calculate the probability
Divide the number of favorable outcomes by the total number of outcomes to find the required probability: P=5010тАЛ which simplifies to 51тАЛ.
P=5010тАЛ=51тАЛ
A is correct because the probability of drawing a ticket that is a multiple of 5 or 10 is 5010тАЛ, which simplifies to 51тАЛ.
Understanding set unions and intersections (inclusion-exclusion principle) is also vital for solving complex Venn diagram and counting questions in quantitative aptitude.