Statistics and Probability MCQs | STA301 MCQs | Set 3

MCQs (Multiple Choice Questions )

1) For two mutually exclusive events A and B, P(A) = 0.2 and P(B) = 0.4,
f then P(A`\cup`B) is:

    a)        0.8

    b)        0.2

    c)        0.6

    d)        0.5

Correct Answer: 

The correct answer is  'c'.

Explanation:

To find the probability of the union of two mutually exclusive events, A and B, we need to consider that mutually exclusive events cannot occur at the same time. In other words, if event A happens, event B cannot happen, and vice versa.

The formula for the union of two mutually exclusive events is:

P(A∪B) = P(A) + P(B)

Since A and B are mutually exclusive, we know that P(A∩B) (the probability of both A and B occurring) is 0.

So, applying the formula:

P(A∪B) = P(A) + P(B) = 0.2 + 0.4 = 0.6

Therefore, the probability of the union of A and B, denoted as P(A∪B), is 0.6.

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2) When two coins are tossed the probability of at most one head is: 

    a)        `1/4`

    b)        `2/4`

    c)        `3/4`

    d)        `4/4`

Correct Answer: 

The correct answer is  'c'.

Explanation:

To find the probability of getting at most one head when two coins are  tossed, we can consider the possible outcomes:

Two tails: This outcome has a probability of `(1/2) * (1/2) = 1/4` since each coin has a `1/2` probability of landing on tails.

One head and one tail: There are two possible ways this can occur: (head, tail) or (tail, head). Each of these outcomes has a probability of `(1/2) * (1/2) = 1/4`. So the total probability for this case is `1/4 + 1/4 = 1/2`.

Adding up the probabilities of the two favorable outcomes (getting two tails and getting one head and one tail), we get:

Probability = `1/4 + 1/2 = 3/4`

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3) A value that has half of the observations above it and half of the observations below it, is known as _________

    a)        Range

    b)        Median

    c)        Mean

    d)        Mode

Correct Answer: 

The correct answer is  'b'.

Explanation:

The median is the middle value in distribution when the values are arranged in ascending or descending order. The median divides the distribution in half (50% of observations are on either side of the median value).

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4) In a set of 20 values all the values are 10, what will be the median?

    a)        2

    b)        5

    c)        10

    d)        20

Correct Answer: 

The correct answer is  'c'.

Explanation:

If all 20 values in the set are 10, the median will also be 10. The median is the middle value when the data is arranged in ascending or descending order. In this case, since all the values are the same, any value you pick from the set will be the middle value, and therefore, the median will be 10.

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5) Which one of the following measures is not based on all the observations?

    a)        Arithmetic Mean

    b)        Geometric Mean

    c)        Harmonic Mean

    d)        Mode

Correct Answer: 

The correct answer is  'd'.

Explanation:

The mode is the value that appears most frequently in a dataset. Unlike the other measures mentioned (arithmetic mean, geometric mean, and harmonic mean), the mode does not take into account all the observations in the dataset. It only focuses on identifying the most common value or values.

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6) 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:

In statistics, the collection of items under study is called population or universe. This includes every element of the study.

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7) A five-number summary consists of :

    a)        `X_0` , `Q_1` , Median , `Q_3` , and `X_m`

    b)        `X_m` , `Q_1` , Mean , `Q_3` , and `X_0`

    c)        `X_m` , `Q_1` , Mode , `Q_3` , and `X_0`

    d)        `X_0` , `Q_1` , Median , `Q_2` , and `X_m`

Correct Answer: 

The correct answer is  'a'.

Explanation:

A five-number summary typically consists of the minimum value (`X_0`), the first quartile (`Q_1`), the median, the third quartile (`Q_3`), and the maximum value (`X_m`). These five values provide a summary of the distribution of a dataset and are commonly used in descriptive statistics and box plots.

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8) For what condition of k, at least `1-1/k^2` of the data-values fall within k standard deviations of the mean:

    a)        Greater than 1

    b)        Less than 1

    c)        Greater or equal to 1

    d)        Less or equal to 1

Correct Answer: 

The correct answer is  'a'.

Explanation:

Chebyshev's inequality says that at least the `1-1/K^2` of data from a sample must fall within K standard deviations from the mean (here K is any positive real number greater than one). 

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9) Which of the following can never be taken as the probability of an event?

    a)        1

    b)        0

    c)        0.5

    d)        -0.5

Correct Answer: 

The correct answer is  'd'.

Explanation:

In probability theory, the probability of an event is a value between 0 and 1, inclusive. Therefore, the only answer choice that cannot be taken as the probability of an event is -0.5.

Negative values are not valid probabilities because probabilities represent the likelihood of an event occurring, and they cannot be negative. The range of probabilities is from 0 (indicating an impossible event) to 1 (indicating a certain event).

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10) If E is an impossible event, then P(E)

    a)        1

    b)        0.15

    c)        0

    d)        0.5

Correct Answer: 

The correct answer is  'c'.

Explanation:

P(E) = 0 if and only if E is an impossible event.

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