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A bag contains 50 tokens numbered 1 to 50. One token is drawn at random. The probability that the number on the token is a multiple of 5 or 10 is:
51тАЛ
101тАЛ
21тАЛ
103тАЛ
51тАЛ
Since every multiple of 10 is already a multiple of 5, the condition 'multiple of 5 or 10' simplifies entirely to multiples of 5.
Total tokens = 50 numbered 1 to 50, drawing one token at random.
P=n(S)n(E)тАЛ
Since every multiple of 10 is already a multiple of 5, the condition 'multiple of 5 or 10' simplifies entirely to multiples of 5.
Adding counts of multiples of 5 and 10 independently without accounting for overlap causes double-counting errors.
Total Outcomes
The total number of tokens in the bag is 50, so the sample space size is n(S)=50.
n(S)=50
Identify Favorable Outcomes
The multiples of 5 between 1 and 50 are 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50, giving 10 numbers. Multiples of 10 are a subset of these, so the union has 10 favorable outcomes.
n(E)=10
Calculate Probability
Substitute the values into the probability formula: P=5010тАЛ=51тАЛ.
P=5010тАЛ=51тАЛ
A is correct because the number of favorable outcomes is 10 out of 50 total outcomes, simplifying to a probability of 51тАЛ.
Recognizing subset relationships in probability prevents unnecessary inclusion-exclusion calculations.