Eleven bags of wheat flour,each marked $5 \,kg$,actually contained the following weights of flour (in $kg$):
$4.97, 5.05, 5.08, 5.03, 5.00, 5.06, 5.08, 4.98, 5.04, 5.07, 5.00$
Find the probability that any of these bags chosen at random contains more than $5 \,kg$ of flour.

$A$ teacher wanted to analyze the performance of two sections of students in a mathematics test of $100$ marks. Looking at their performances,she found that a few students got under $20$ marks and a few got $70$ marks or above. So she decided to group them into intervals of varying sizes as follows: $0-20, 20-30, ..., 60-70, 70-100$. Then she formed the following table:

Marks	Number of students
$0-20$	$7$
$20-30$	$10$
$30-40$	$10$
$40-50$	$20$
$50-60$	$20$
$60-70$	$15$
$70$ and above	$8$
Total	$90$

$(i)$ Find the probability that a student obtained less than $20\%$ in the mathematics test.
$(ii)$ Find the probability that a student obtained marks $60$ or above.

On one page of a telephone directory,there were $200$ telephone numbers. The frequency distribution of their unit place digit (for example,in the number $25828573$,the unit place digit is $3$) is given in the table below:

Digit	$0, 1, 2, 3, 4, 5, 6, 7, 8, 9$
Frequency	$22, 26, 22, 22, 20, 10, 14, 28, 16, 20$

Without looking at the page,a number is chosen at random. What is the probability that the digit in its unit place is $6$?

$1500$ families with $2$ children were selected randomly,and the following data were recorded:

Number of girls in a family	$2$	$1$	$0$
Number of families	$475$	$814$	$211$

Compute the probability of a family,chosen at random,having:
$(i)$ $2$ girls $(ii)$ $1$ girl $(iii)$ No girl
Also,check whether the sum of these probabilities is $1$.

The distance (in $km$) of $40$ engineers from their residence to their place of work were found as follows.

$5$	$3$	$10$	$20$	$25$	$11$	$13$	$7$	$12$	$31$
$19$	$10$	$12$	$17$	$18$	$11$	$32$	$17$	$16$	$2$
$7$	$9$	$7$	$8$	$3$	$5$	$12$	$15$	$18$	$3$
$12$	$14$	$2$	$9$	$6$	$15$	$15$	$7$	$6$	$12$

What is the empirical probability that an engineer lives:
$(i)$ less than $7 \, km$ from her place of work?
$(ii)$ more than or equal to $7 \, km$ from her place of work?
$(iii)$ within $\frac{1}{2} \, km$ from her place of work?

$A$ die is thrown $1000$ times with the frequencies for the outcomes $1, 2, 3, 4, 5$ and $6$ as given in the following table:

Outcome	$1$	$2$	$3$	$4$	$5$	$6$
Frequency	$179$	$150$	$157$	$149$	$175$	$190$

Find the probability of getting each outcome.