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:

Table

Without looking at the page, the pencil is placed on one of these numbers, i.e., the number is chosen at random. What is the probability that the digit in its unit place is 6?

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 tyre manufacturing company kept a record of the distance covered before a tyre needed to be replaced. The table shows the results of 1000 cases.  [CBSE 2012 (March)]

Table

If you buy a tyre of this company, what is the probability that:

(i) it will need to be replaced before it has covered 400 km?
(ii)  it will last more than 900 km?
(iii)  it will need to be replaced after it has covered somewhere between 400 km andb 1400 km?
(iv)  it will not need to be replaced at all?
(v)  it will need to be replaced?

The percentage of marks obtained by a student in the monthly unit tests are given below:
Table

Based on this data, find the probability that the student gets more than 70% marks in a unit test.

An insurance company selected 2000 drivers at random (i.e., without any preference of one driver over another) in a particular city to find a relationship between age and accidents. The data obtained are given in the following table:

Table

Find the probabilities of the following events for a driver chosen at random from the city:

(i) being 18–29 years of age and having exactly 3 accidents in one year.
(ii)  being 30-50 years of age and having one or more accidents in a year.
(iii)  having no accidents in one year.

Consider the following frequency distribution table, which gives the weights of 38 students of a class:

(i)  Find the probability that the weight of a student in the class lies in the interval 46-50 kg.

(ii)  Give two events in this context, one having probability 0 and the other having probability 1:

Table

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:

Table

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?

Two coins are tossed simultaneously 1000 times with the following frequencies of different outcomes.

If these two coins are tossed again, find the probability of getting

(i)  at least 1 head
(ii)  at most 1 head

Two coins are tossed simultaneously 500 times,

and we get

Find the probability of occurrence of

(i)  two heads
(ii)  all tails.

40.

These coins are tossed simultaneously 200 times with the following frequencies of different outcomes:

Outcome	Frequency
3 heads	24
2 heads	70
1 head	75
3 tails	31

Compute the probability of getting

(i)  less than 2 heads
(ii)  3 heads.