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Karnataka SSLC (Class 10) Statistics and Probability — practice questions — page 3

Explore 85 free Statistics and Probability questions in Karnataka SSLC (Class 10) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Statistics and Probability questions and exercises with answers

Showing questions 61–85 of 85.

On a less-than ogive, the median is read off by drawing a horizontal line at:Read the answer and worked solution →A cumulative frequency table's final entry equals:Read the answer and worked solution →Probability of any event satisfies:Read the answer and worked solution →P(not A) equals:Read the answer and worked solution →Distance between (1, 2) and (4, 6) equals:Read the answer and worked solution →Midpoint of A(2, 4) and B(6, 10) is:Read the answer and worked solution →Mean of 5 numbers is 12. Their sum equals:Read the answer and worked solution →For an even number of sorted values, the median is:Read the answer and worked solution →CLASS10 · Mathematics · Distance Formula — Gap FillRead the answer and worked solution →CLASS10 · Mathematics · Mean, Median, ModeRead the answer and worked solution →CLASS10 · Mathematics · Probability — BasicsRead the answer and worked solution →CLASS10 · Mathematics · Statistics — True or FalseRead the answer and worked solution →SAT · Mathematics · Slope from Two Points — Gap FillRead the answer and worked solution →The probability of an event $E$ is defined asRead the answer and worked solution →The probability of a sure (certain) event isRead the answer and worked solution →The probability of an impossible event isRead the answer and worked solution →The probability $P(E)$ of any event always liesRead the answer and worked solution →For an event $E$ and its complement $\overline{E}$ (not E),Read the answer and worked solution →The probability of getting a head when a fair coin is tossed once isRead the answer and worked solution →A die is rolled once. The probability of getting the number 3 isRead the answer and worked solution →A die is rolled once. The probability of getting an even number isRead the answer and worked solution →If $P(E) = 0.35$, then $P(\text{not } E)$ isRead the answer and worked solution →One card is drawn from a well-shuffled deck of 52 cards. The probability that it is a red card isRead the answer and worked solution →A bag has 3 red and 2 blue balls. The probability of drawing a red ball at random isRead the answer and worked solution →A die is rolled once. The probability of getting a number less than 7 isRead the answer and worked solution →

Worked practice questions

On a less-than ogive, the median is read off by drawing a horizontal line at:

  1. y = n/3
  2. y = n/2
  3. y = n/4
  4. y = n
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Correct answer: B. y = n/2

Median splits the data in half — so the horizontal line is at y = n/2, and the x-intercept where it meets the curve is the median.

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A cumulative frequency table's final entry equals:

  1. the total frequency
  2. the modal frequency
  3. zero
  4. half the total
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Correct answer: A. the total frequency

By definition, the last cumulative frequency = sum of all individual frequencies = total number of observations.

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Probability of any event satisfies:

  1. 0 ≤ P ≤ 1
  2. 0 ≤ P ≤ 100
  3. −1 ≤ P ≤ 1
  4. P ≥ 1
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Correct answer: A. 0 ≤ P ≤ 1

The probability of an event $E$, denoted as $P(E)$, is defined as the ratio of the number of favorable outcomes to the total number of outcomes in a sample space. 1. **Minimum Value**: The smallest number of favorable outcomes is $0$ (this happens when the event is impossible). Therefore, the minimum probability is: $$P(E) = \frac{0}{n} = 0$$ 2. **Maximum Value**: The largest number of favorable outcomes is equal to the total number of outcomes $n$ (this happens when the event is certain). Therefore, the maximum probability is: $$P(E) = \frac{n}{n} = 1$$ 3. **Conclusion**: Since the number of favorable outcomes $m$ must satisfy $0 \leq m \leq n$, it follows that dividing by $n$ gives: $$\frac{0}{n} \leq \frac{m}{n} \leq \frac{n}{n}$$ $$0 \leq P(E) \leq 1$$ Thus, the probability of any event must be between 0 and 1, inclusive.

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