State whether each of the following statements is true or false:
$(1)$ The probability that the month of February in a leap year has $5$ Saturdays is $0$.
$(2)$ The probability of getting $51$ marks in a $100$ marks examination is $\frac{1}{101}$.
$(1)$ The probability that the month of February in a leap year has $5$ Saturdays is $0$.
$(2)$ The probability of getting $51$ marks in a $100$ marks examination is $\frac{1}{101}$.
(B) $(1)$ False. In a leap year,February has $29$ days. $29$ days consist of $4$ weeks and $1$ extra day. The extra day can be any of the $7$ days of the week. The probability of this extra day being a Saturday is $\frac{1}{7}$,which is not $0$.
$(2)$ False. In an examination of $100$ marks,the possible marks are integers from $0$ to $100$. There are $101$ possible outcomes $(0, 1, 2, ..., 100)$. Assuming each mark is equally likely,the probability of getting exactly $51$ marks is $\frac{1}{101}$.
$(2)$ False. In an examination of $100$ marks,the possible marks are integers from $0$ to $100$. There are $101$ possible outcomes $(0, 1, 2, ..., 100)$. Assuming each mark is equally likely,the probability of getting exactly $51$ marks is $\frac{1}{101}$.
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