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Published on: 18/09/2019
Probability
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1.
There are 13 girls and 15 boys in a line. If one student is chosen at random, then find the probability that he is a boy.
2.
The probability of winning a game is \(\frac{1}{3}\) less than the twice of losing the game. Find probability of winning the game.
3.
On a particular day, the number of vehicles passing through a crossing is given below:
| Vehicle | 2 wheeler | 3 wheeler | 4 wheeler |
| Frequency | 57 | 33 | 30 |
A particular vehicle is chosen at random. What is the probability that it is not a four wheeler?
4.
Two coins are tossed simultaneously 500 times, following are the outcomes
No head = 100 times
One head = 200 times
Two heads = 200 times
If the two coins are simultaneously tossed agian, compute the probability of obtaining:
(i) One Head
(ii) Two Head
5.
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.
| Distance(in km) | less than 400 |
400 to 900 | 900 to 1400 | more than 1400 |
| Frequency | 210 | 325 | 385 | 80 |
If you buy a tyre of this company, what is the probability that:
(i) it will need to be replaced before it has covered 400km?
(ii) it will last more than 900 km?
(iii) it will need to be replaced after it has covered somewhere between 400 km and 1400 km?
(iv) it will not need to be replaced at all?
(v) it will need to be replaced?
6.
A bag contains 190 coins out of which, fifty Rs 2 coins, forty Rs 1 coins and rest Rs 5 coins. One coin is selected at random. Find the probability that it is a Rs 5 coin.
7.
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
| Weights(in kg) | Number of students |
| 31-35 | 9 |
| 36-40 | 5 |
| 41-45 | 14 |
| 46-50 | 3 |
| 51-55 | 1 |
| 56-60 | 2 |
| 61-65 | 2 |
| 66-70 | 1 |
| 71-75 | 1 |
| Total | 38 |
8.
Cards marked with numbers 2, 3, 4, ..., 61 are placed in a box and mixed thoroughly. One card is drawn. Find the probability that card drawn is
(i) an even number
(ii) a square number
9.
A die is thrown 1000 times with the following frequencies for the outcomes 1,2,3,4,5and 6 as given below:
| Outcome | Frequency |
| 1 | 175 |
| 2 | 125 |
| 3 | 250 |
| 4 | 150 |
| 5 | 100 |
| 6 | 200 |
If the same die is thrown once more, find the probability of outcome 2, 4 and 6.
10.
In a box, there are 9 red, 8 white, and 3 black balls. One ball is taken out of the bag. Find the probability that it is
(i) white
(ii) red or black
(iii) not red.
11.
A bag has 3 red and 7 black balls. One ball is taken out of the bag. Find the probability that it is a
(i) red ball
(ii) blackball.
12.
Three 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.
13.
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?
14.
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, 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?
15.
In a cricket match, a batsman hits boundary in 20% of the balls he played. Find the probability that he did not hit a boundary.
1.
Number of Boys = 15
NUmber of Girls = 13
\(\therefore \)Total Number of Student = 15 +13 = 28
Probability of selecting a boy\(=\frac{15}{28}\)
2.
Let the probability of winning a game = p
and probability of losing a game = q
we know that p + q = 1...(i)
According to questions,
\(p=2q-\frac{1}{3}\)
\(\Rightarrow \) 6q - 3p = 1...(ii)
On solving (i) and (ii), we get
\(q=\frac{4}{9}\ and\ p=\frac{5}{9}\)
\(\therefore \) Probability of winning game \(=\frac{5}{9}\)
3.
Total number of vehicles = 57 + 33 + 30 = 120
Vehicles which are not four wheelers = 57 + 33 = 90
\(\therefore \)P(chosen vehicle is not four wheeler)\(=\frac{90}{120}=\frac{3}{4}\)
4.
Total number of outcomes = 500
Let E1 and E2 be the events of one head and twp heads respectively.
\(P(E_1)=\frac{200}{500}=\frac{2}{5}\)
\(P(E_2)=\frac{200}{500}=\frac{2}{5}\)
5.
(i) 0.21
(ii) 0.465
(iii)0.79 (iv)0 (v) 1
6.
\(\frac { 10 }{ 19 } \)
7.
(i) The total number of students is 38, and the number of students with weight in the interval 46 - 50 kg is 3.
So, P(weight of a student is in the interval 46 - 50 kg) = \(\frac{3}{38}=0.079\)
(ii) For instance, consider the event that a student weighs 30 kg. Since no student has this weight, the probability of occurrence of this event is 0. Similarly, the probability of a student weighing more than 30 kg is \(\frac{38}{38}=1\)
8.
\((i)\frac { 1 }{ 2 } \)
\((ii)\frac { 1 }{ 10 } \)
9.
\((i)\frac { 1 }{ 8 }\)
\((ii)\frac { 3 }{ 20 }\)
\((iii)\frac { 1 }{ 5 } \)
10.
\((i)\frac { 2 }{ 5 }\)
\((ii)\frac { 3 }{ 5 } \)
\((iii)\frac { 11 }{ 20 } \)
11.
\((i)\frac { 3 }{ 10 }\)
\((ii)\frac { 7 }{ 10 } \)
12.
\((i)\frac { 53 }{ 100 }\)
\((ii)\frac { 3 }{ 25 } \)
13.
The total number of days for which the record is available = 250
(i) P(the forecast was correct on a given day)
\(
=\frac{\text { Number of days when the forecast was correct }}{\text { Total number of days for which the record is available }}
\)
\(=\frac{175}{250}=0.7\)
(ii) The number of days when the forecast was not correct = 250 - 175 = 75
So, P(the forecast was not correct on a given day) \(=\frac{75}{250}=0.3\)
14.
The probability of digit 6 being in the unit place
\(
=\frac{\text { Frequency of } 6}{\text { Total number of selected telephone numbers }}
\)
\(=\frac{14}{200}=0.07
\)
15.
Hits boundary = 20% of balls
Does not hit boundarty = 80% of balls
\(\therefore \) P(not hitting boundary) = \(\frac{80}{100}=\frac{4}{5}\)
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