CBSE Class 7 Mathematics Data Handling Assignment Set 04

VII - Mathematics Assignment No - 05 - Data Handling

Q1. A dice is tossed once, Find the probability of
(i) Even number
(ii) Odd number
(iii) Prime number
Answer:
Total possible outcomes when a die is tossed = 6 (Outcomes are 1, 2, 3, 4, 5, 6)
(i) Even numbers on a die are 2, 4, 6 (Total = 3)
Probability of getting an even number = \(\frac{3}{6} = \frac{1}{2}\)
(ii) Odd numbers on a die are 1, 3, 5 (Total = 3)
Probability of getting an odd number = \(\frac{3}{6} = \frac{1}{2}\)
(iii) Prime numbers on a die are 2, 3, 5 (Total = 3)
Probability of getting a prime number = \(\frac{3}{6} = \frac{1}{2}\)
In simple words: The total number of possible faces on a die is 6. For each sub-part, we count the favorable outcomes and divide by 6.

Exam Tip: Remember that 1 is neither prime nor composite. Always reduce fractions to their simplest form.

Q2. What is the probability of selecting the letter 'D' from the word "Assured".
Answer:
Total letters in the word "Assured" = 7
Number of times the letter 'D' appears = 1
Probability of selecting the letter 'D' = \(\frac{1}{7}\)
In simple words: Count all the letters in the given word for the denominator, and count how many times 'D' appears for the numerator.

Exam Tip: Count duplicate letters individually based on their exact positions unless specified otherwise.

Q3. In a Cricket match between India and Pakistan, what is the probability of winning the toss?
Answer:
Total possible outcomes for a toss (Heads or Tails) = 2
Favorable outcome of winning the toss = 1
Probability of winning the toss = \(\frac{1}{2}\)
In simple words: A coin toss has 2 outcomes (Head or Tail), so any team has 1 chance out of 2 to win the toss.

Exam Tip: Team names are extra information and do not affect the probability of a fair coin toss.

Q4. What is the probability of getting a vowel from the word "EQUATION".
Answer:
Total letters in the word "EQUATION" = 8
Vowels in the word "EQUATION" are E, U, A, I, O (Total = 5)
Probability of getting a vowel = \(\frac{5}{8}\)
In simple words: Count the total letters for the bottom number, and count how many vowels (A, E, I, O, U) are in the word for the top number.

Exam Tip: Double-check all vowels in the given word so none are missed.

Q5. What is the probability of picking a month from the year having 30 days?
Answer:
Total months in a year = 12
Months having 30 days are April, June, September, November (Total = 4)
Probability = \(\frac{4}{12} = \frac{1}{3}\)
In simple words: There are 12 months in total, and 4 of them have exactly 30 days. Simplify 4 out of 12 to 1 out of 3.

Q6. What is the probability of choosing a prime number from 0, 1, 2, 3, 4, 5.
Answer:
Total numbers given = 6 (0, 1, 2, 3, 4, 5)
Prime numbers among them = 2, 3, 5 (Total = 3)
Probability = \(\frac{3}{6} = \frac{1}{2}\)
In simple words: Out of the 6 given numbers, 2, 3, and 5 are prime numbers. Thus, the probability is 3 divided by 6.

Exam Tip: Zero and one are not prime numbers. The lowest prime number is 2.

Q7. A dice is tossed 15 times. The number 2 appears 5 times. Number 6 appears 7 times, etc. What is the probability of getting the number 6?
Answer:
Total number of trials (total tosses) = 15
Number of times the number 6 appeared = 7
Probability of getting the number 6 = \(\frac{7}{15}\)
In simple words: Use experimental probability where the number of favorable occurrences is divided by the total number of trials.

Exam Tip: In experimental probability, always use the given number of trials as the denominator instead of 6.

Q8. A bag contains 5 Red and 6 black balls. A ball is drawn at random. Which coloured ball has more chances to come?
Answer:
Number of red balls = 5
Number of black balls = 6
Since 6 > 5, black balls are greater in quantity.
Therefore, Black coloured ball has more chances to come.
In simple words: The color with the higher count in the bag has a higher probability of being drawn.

Exam Tip: Compare the quantities directly; higher quantity means higher chance without needing to calculate exact fractions.

Q9. What is the probability of drawing an odd number from the first 15 natural numbers.
Answer:
First 15 natural numbers are 1 to 15 (Total = 15)
Odd numbers from 1 to 15 are 1, 3, 5, 7, 9, 11, 13, 15 (Total = 8)
Probability = \(\frac{8}{15}\)
In simple words: There are 15 natural numbers in total, out of which 8 are odd numbers.

Exam Tip: Natural numbers start from 1, not 0.

Q10. A coin is tossed once, what is the probability of head if it is given the probability of tail is \(\frac{1}{2}\)?
Answer:
Let \(P(H)\) be the probability of getting a head and \(P(T)\) be the probability of getting a tail.
We know that \(P(H) + P(T) = 1\)
Given \(P(T) = \frac{1}{2}\)
\(P(H) = 1 - \frac{1}{2} = \frac{1}{2}\)
In simple words: The sum of probabilities of all possible outcomes is always 1. Subtracting the probability of tail from 1 gives the probability of head.

Exam Tip: Use the complementary probability property \(P(E) + P(\text{not } E) = 1\) for quick solutions.