$A$ coin is tossed $1000$ times with the following frequencies:
Head : $455$ Tail : $545$
Compute the probability for each event.

The record of a weather station shows that out of the past $250$ consecutive days,its weather forecasts were correct $175$ times.
$(i)$ What is the probability that on a given day it was correct?
$(ii)$ What is the probability that it was not correct on a given day?

$A$ 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.

Fifty seeds were selected at random from each of $5$ bags of seeds,and were kept under standardised conditions favourable to germination. After $20$ days,the number of seeds which had germinated in each collection were counted and recorded as follows:

Bag	$1$	$2$	$3$	$4$	$5$
Number of seeds germinated	$40$	$48$	$42$	$39$	$41$

What is the probability of germination of
$(i)$ more than $40$ seeds in a bag?
$(ii)$ $49$ seeds in a bag?
$(iii)$ more than $35$ seeds in a bag?

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.

The following frequency distribution table shows the blood groups of $30$ students of a class. Use this table to determine the probability that a student of this class,selected at random,has blood group $AB$.

Blood group	Number of students
$A$	$9$
$B$	$6$
$AB$	$3$
$O$	$12$
Total	$30$