$A$ box contains $100$ cards marked with numbers $1$ to $100$. If one card is drawn at random from the box,find the probability that the number on the card is: $(1)$ a multiple of $7$,$(2)$ a number smaller than $30$,$(3)$ a prime number.
(N/A) Total number of cards $n(S) = 100$.
$(1)$ Multiples of $7$ between $1$ and $100$ are ${7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98}$. There are $14$ such numbers. Probability $P = 14/100 = 0.14$.
$(2)$ Numbers smaller than $30$ are ${1, 2, 3, dots, 29}$. There are $29$ such numbers. Probability $P = 29/100 = 0.29$.
$(3)$ Prime numbers between $1$ and $100$ are ${2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}$. There are $25$ such numbers. Probability $P = 25/100 = 0.25$.
$(1)$ Multiples of $7$ between $1$ and $100$ are ${7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98}$. There are $14$ such numbers. Probability $P = 14/100 = 0.14$.
$(2)$ Numbers smaller than $30$ are ${1, 2, 3, dots, 29}$. There are $29$ such numbers. Probability $P = 29/100 = 0.29$.
$(3)$ Prime numbers between $1$ and $100$ are ${2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}$. There are $25$ such numbers. Probability $P = 25/100 = 0.25$.
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