One card is selected at random from 27 cards | vedclass

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(B) Total number of cards $n(S) = 27$. Let $E$ be the event that the number is even. The even numbers between $1$ and $27$ are $\{2, 4, 6, 8, 10, 12,

Vedclass · Accepted Answer

$\frac{16}{27}$

Vedclass · Answer

(B) Total number of cards $n(S) = 27$. Let $E$ be the event that the number is even. The even numbers between $1$ and $27$ are $\{2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26\}$. Thus,$n(E) = 13$. Let $F$ be the event that the number is divisible by $5$. The numbers divisible by $5$ are $\{5, 10, 15, 20, 25\}$. Thus,$n(F) = 5$. The intersection $E \cap F$ contains numbers that are both even and divisible by $5$,which are multiples of $10$. These are $\{10, 20\}$. Thus,$n(E \cap F) = 2$. Using the addition rule for probability,$n(E \cup F) = n(E) + n(F) - n(E \cap F) = 13 + 5 - 2 = 16$. The probability is $P(E \cup F) = \frac{n(E \cup F)}{n(S)} = \frac{16}{27}$.

One card is selected at random from $27$ cards numbered from $1$ to $27$. What is the probability that the number on the card is even or divisible by $5$?

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