A coin is tossed 1000 times with the following frequencies:
Head: 455, Tail: 545 compute the probability for each event.
Two coins are tossed simultaneously 500 times, and we get- Two heads: 105 times, One head: 275 times, No head: 120 times, find the probability of occurrence of each of these events.
A die is thrown 1000 times with the frequencies for the outcome 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
1175
190
Find the probability of getting each outcome.
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?
The percentage (%) of the marks obtained by a student in the monthly unit test are given below:
Unit test
I
II
III
IV
V
Percentage (%) of the marks obtained
69
71
73
68
74
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:
Age of drivers
(in years
Accidents in one year
0
1
2
3
Over 3
18-29
440
160
110
61
35
30-50
505
125
60
22
18
Above 50
360
45
35
15
9
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.
In a cricket match, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary.
1500 families with 2 children were selected randomly, and the following data were recorded:
Numbers 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.
Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:
Outcome
3 heads
2 heads
1 head
No head
Frequency
23
72
77
28
If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.
An organization selected 2400families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family, the information gathered is listed in the table below:
Monthly in come
(in Rs)
Vehicles per family
0
1
2
Above 2
Less than 7000
10
160
25
0
7000-10000
0
305
27
2
10000-13000
1
535
29
1
13000-16000
2
469
59
25
16000 or more
1
579
82
88
Suppose a family is chosen. Find the probability that the family chosen is
(i) Earning Rs 10000-13000 per month and owing exactly 2 vehicles.
(ii) Earning Rs 16000 or more per month and owning exactly 1 vehicle.
(iii) Earning less than Rs 7000 per month and does not own any vehicle.
(iv) Earning Rs 13000-16000 per month and owning more than 2 vehicles.
(v) Owning not more than 1 vehicle.
Eleven bags of wheat flour, each marked 5 kg, actually contained 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.
