There are 100 lottery tickets numbered from 1 | vedclass

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(C) Let $A$ be the event that the number on the ticket is a multiple of $3$.Let $B$ be the event that the number on the ticket is a multiple of $5$.Th

Vedclass · Accepted Answer

$47/100$

Vedclass · Answer

(C) Let $A$ be the event that the number on the ticket is a multiple of $3$.Let $B$ be the event that the number on the ticket is a multiple of $5$.The multiples of $3$ up to $100$ are $A = \{3, 6, 9, \dots, 99\}$,so $n(A) = 33$.The multiples of $5$ up to $100$ are $B = \{5, 10, 15, \dots, 100\}$,so $n(B) = 20$.The multiples of both $3$ and $5$ (i.e.,multiples of $15$) are $A \cap B = \{15, 30, 45, 60, 75, 90\}$,so $n(A \cap B) = 6$.Using the addition theorem of probability,$P(A \cup B) = P(A) + P(B) - P(A \cap B)$.$P(A \cup B) = \frac{33}{100} + \frac{20}{100} - \frac{6}{100} = \frac{47}{100}$.

There are $100$ lottery tickets numbered from $1$ to $100$. If a ticket is drawn at random,find the probability that the number on it is a multiple of $3$ or $5$.

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