VSAQS
Page-25.18
Question 1:
Define a trial.
Answer 1:
What is the meaning of trial?
The word trial means a test of performance, qualities, or suitability.
Definition:
Any particular performance of a random experiment is called a trial. That is, when we perform an experiment it is called a trial of the experiment.
By experiment or trial, we mean a random experiment unless otherwise specified. Where you are required to differentiate between a trial and an experiment, consider the experiment to be a larger entity formed by the combination of a number of trials.
To illustrate the definition, let us take examples:
1. In the experiment of tossing 4 coins, we may consider tossing each coin as a trial and therefore say that there are 4 trials in the experiment.
2. In the experiment of rolling a dice 5 times, we may consider each rolls as a trial and therefore say that there are 5 trials in the experiment.
Note that rolling a dice 5 times is same as rolling 5 dices each one time. Similarly, tossing 4 coins is same as tossing one coin 4 times.
Question 2:
Define an elementary event.
Answer 2:
What are the meanings of elementary event?
The word elementary means simple, non decomposable into elements or other primary constituents and the word event means something that result.
Definition:
An elementary event is any single outcome of a trial. Elementary events are also called simple events.
To illustrate the definition, let us take examples:
1. In the experiment of tossing a coin, the possible outcomes H and T. Any one outcome like H is called an elementary event.
2. In the experiment of rolling a dice, the possible outcomes are 1, 2, 3, 4, 5 and 6. Any one outcome like 4 is called an elementary event.
Note that H stands for getting a head and T stands for getting a tail in the experiment of tossing a coin.
Question 3:
Define an event.
Answer 3:
What are the meanings of event?
The word event means something that result.
Definition:
An event is a collection of outcomes of a trial of a random experiment.
To illustrate the definition, let us take examples:
1. When two coins are tossed simultaneously, the possible outcomes are HH, HT, TH and TT. Any one outcome like HH is called an event (elementary event). The collections like {HH, HT}, {HH, HT, TT} etc are all events (compound event).
2. In the experiment of rolling a dice, the possible outcomes are 1, 2, 3, 4, 5 and 6. Any one outcome like 4 is called an event (elementary event). The collections like {1, 2}, {1, 2, 3}, {2, 5, 6}, {2, 3, 4, 5} etc are all events (compound events).
Note that H stands for getting a head and T stands for getting a tail in the experiment of tossing a coin.
Question 4:
Define probability of an event.
Answer 4:
The probability of an event denotes the relative frequency of occurrence of an experiment’s outcome, when repeating the experiment.
Definition:
The empirical or experimental definition of probability is that if n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials, then the probability of happening of event A is denoted by
and is given by
To illustrate the definition, let us take examples:
1. When two coins are tossed simultaneously, the possible outcomes are HH, HT, TH and TT. The total number of trials is 4. Let A be the event of occurring exactly two heads. The number of times A happens is 1. So, the probability of the event A is
2. In the experiment of rolling a dice, the possible outcomes are 1, 2, 3, 4, 5 and 6. Let A be the event of occurring a number greater than 3. The total number of trials is 6. The number of times A happens is 3. So, the probability of the event A is
Note that H stands for getting a head and T stands for getting a tail in the experiment of tossing a coin.
Question 5:
A big contains 4 white balls and some red balls. If the probability of drawing a white ball from the bag is , find the number of red balls in the bag.
Answer 5:
The number of white balls is 4. Let the number of red balls is x. Then the total number of trials is
.
Let A be the event of drawing a white ball.
The number of times A happens is 4.
Remember the empirical or experimental or observed frequency approach to probability.
If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by
Therefore, we have
.
But, it is given that
. So, we have
Hence the number of red balls is
.
Question 6:
A die is thrown 100 times. If the probability of getting an even number is . How many times an odd number is obtained?
Answer 6:
The total number of trials is 100. Let the number of times an even number is obtained is x.
Let A be the event of getting an even number.
The number of times A happens is x.
Remember the empirical or experimental or observed frequency approach to probability.
If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by
Therefore, we have
.
But, it is given that. So, we have
Hence an even number is obtained 40 times. Consequently, an odd number is obtained
times.
Question 7:
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 |
Find the probability of getting at most two heads.
Answer 7:
The total number of trials is 200.
Let A be the event of getting at most two heads.
The number of times A happens is
.
Remember the empirical or experimental or observed frequency approach to probability.
If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by
Therefore, we have
.
Question 8:
In Q.No. 7, what is the probability of getting at least two heads?
Answer 8:
The total number of trials is 200.
Let A be the event of getting atleast two heads.
The number of times A happens is
.
Remember the empirical or experimental or observed frequency approach to probability.
If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by
Therefore, we have
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