One ticket is drawn at random out of 30 ticke | vedclass

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(B) The total number of tickets is $30$,so the sample space $S = \{1, 2, 3, \ldots, 30\}$ and $n(S) = 30$.Let $A$ be the event of drawing a ticket wit

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$\frac{1}{3}$

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(B) The total number of tickets is $30$,so the sample space $S = \{1, 2, 3, \ldots, 30\}$ and $n(S) = 30$.Let $A$ be the event of drawing a ticket with a number that is a multiple of $5$.$A = \{5, 10, 15, 20, 25, 30\}$,so $n(A) = 6$.Let $B$ be the event of drawing a ticket with a number that is a multiple of $7$.$B = \{7, 14, 21, 28\}$,so $n(B) = 4$.Since $A$ and $B$ are mutually exclusive events (there are no common multiples of $5$ and $7$ up to $30$),the probability of $A$ or $B$ is given by $P(A \cup B) = P(A) + P(B)$.$P(A) = \frac{n(A)}{n(S)} = \frac{6}{30}$.$P(B) = \frac{n(B)}{n(S)} = \frac{4}{30}$.Therefore,$P(A \cup B) = \frac{6}{30} + \frac{4}{30} = \frac{10}{30} = \frac{1}{3}$.

One ticket is drawn at random out of $30$ tickets numbered from $1$ to $30.$ Find the probability that the number on the ticket is a multiple of $5$ or $7.$

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