Statistics and Probability MCQs | STA301 MCQs | Set 1
Statistics and Probability MCQs | STA301 MCQs | Set 1
MCQs (Multiple Choice Questions)
1) The probability of drawing a 'white' ball from containing 4 red, 8
black, and 3 white balls is:
a) 0
b) `3/15`
c) `1/12`
d) `1/2`
Correct Answer:
The correct answer is 'b'.
Explanation:
To calculate the probability of drawing a 'white' ball from a container containing 4 red, 8 black, and 3 white balls, we need to consider the total number of balls and the number of 'white' balls in the container.
The total number of balls in the container is 4 + 8 + 3 = 15.
The number of 'white' balls in the container is 3.
Therefore, the probability of drawing a 'white' ball can be calculated
as:
Probability = Number of white balls / Total number of balls
Probability = `3/15`
Simplifying the fraction, we get:
Probability = `1/5`
So, the probability of drawing a 'white' ball from the container is `3/15` or `1/5` or 0.2, which can also be expressed as 20%.
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2) if the probability of one event does not affect by the occurrence of another event then both events are:
a) Dependent
b) Not Mutually Exclusive
c) Mutually Exclusive
d) Independent
Correct Answer:
The correct answer is 'd'.
Explanation:
If the probability of one event is not affected by the occurrence of another event, then both events are considered to be independent. In other words, the outcome or probability of one event does not change or influence the outcome or probability of the other event.
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3) A die is rolled. What is the probability of getting a number that is an even number and greater than 2?
a) `1/2`
b) `1/3`
c) `2/3`
d) `5/6`
Correct Answer:
The correct answer is 'b'.
Explanation:
To calculate the probability of rolling a die and getting a number that
is both even and greater than 2, we need to determine the favorable
outcomes and the total number of possible outcomes.
The favorable outcomes are the numbers on the die that satisfy both
conditions: being even and greater than 2. These numbers are 4 and
6.
The total number of possible outcomes when rolling a die is 6 since there are six faces with numbers 1 to 6.
Therefore, the probability can be calculated as:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 2 / 6
Simplifying the fraction, we get:
Probability = 1 / 3
So, the probability of rolling a die and getting a number that is both even and greater than 2 is 1/3 or approximately 0.333, which can also be expressed as approximately 33.33%.
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4) The collection of all the elements under study is called:
a) Population
b) Sample
c) Data
d) Registration
Correct Answer:
The correct answer is 'a'.
Explanation:
The collection of all the elements under study is called a
"population."
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5) The made value from raw data can be obtained with the help of:
a) Dot plot
b) Stem and leaf plot
c) Bar chart
d) All of these
Correct Answer:
The correct answer is 'b'.
Explanation:
Each of these graphical tools can be used to represent and analyze raw
data, depending on the type and characteristics of the data.
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6) A student solved 25 questions from the first 50 questions of a book.
The
probability that he will solve the remaining all questions is :
a) 0.25
b) 0.5
c) 1
d) 0
Correct Answer:
The correct answer is 'b'.
Explanation:
To calculate the probability of solving of remaining question from the first 50 questions of a book:
The total number of questions = 50.
The number of solved questions = 25.
The number of remaining questions = 25.
Therefore, the probability of the remaining questions can be calculated as:
Probability = Number of remaining questions / Total number of questions
Probability = `25/50`
Simplifying the fraction, we get:
Probability = `1/2`
So, the probability of drawing a 'white' ball from the container is `1/2`
or 0.5, which can also be expressed as 20%.
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7) The difference between the largest and the smallest data
values
is called the:
a) Variance
b) Interquartile
range
c) Range
d) Coefficient of variation
Correct Answer:
The correct answer is 'c'.
Explanation:
The difference between the largest and the smallest data values is called the "Range."
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8) Which one is the formula of the mid-quartile range:
a) `Q_3 - Q_1`
b) `{Q_3 - Q_1}/2`
c) `{Q_1 - Q_3}/2`
d) `{Q_1 + Q_3}/2`
Correct Answer:
The correct answer is 'd'.
Explanation:
The mid-quartile range is the numerical value midway between the first and third quartile. It is one-half the sum of the first and third quartiles. It is obtained by evaluating `{Q_3+Q_1}/2`
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9) For the given data 2, 3, 7, 0, -8; G.M. will be:
a) Negative
b) Positive
c) Zero
d) Undefined
Correct Answer:
The correct answer is 'c'.
Explanation:
Since one of the data is 0, the product of all of them is 0, so the G.M. is 0.
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10) Mean deviation is least when calculated from:
a) Mean
b) Mode
c) Median
d) Geometric Mean
Correct Answer:
The correct answer is 'c'.
Explanation:
The mean deviation is calculated either from the mean or median, but only the median is preferred because when the signs are ignored, the sum of the deviation of the sets taken from the median is minimum.
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