CBSE Class 7 Mathematics Data Handling Assignment Set 05

Q1. Write the Sample Space when a coin is tossed (i) once (ii) two times.
[Hint : Sample Space means, total outcomes recorded in an experiment]
Answer: (i) When a coin is tossed once, the sample space is \(\{H, T\}\).
(ii) When a coin is tossed two times, the sample space is \(\{HH, TT, HT, TH\}\).
In simple words: The sample space is simply the complete list of all possible results you can get from an experiment.

Exam Tip: Always enclose the set of outcomes inside curly brackets \(\{ \}\) and separate elements with commas.

Q2. Write the Sample Space when a dice is tossed once.
Answer: A standard die has 6 faces numbered from 1 to 6.
Sample space = \(\{1, 2, 3, 4, 5, 6\}\)
In simple words: All possible numbers that can show up on the top face of a standard die are 1, 2, 3, 4, 5, and 6.

Exam Tip: Remember that a standard die contains the numbers 1 through 6, unless stated otherwise.

Q3. A Box contains 4 white marbles and 3 black marbles. Write its sample space if one marble is taken out at a time. Write W for white marbles and B for black marbles.
Answer: There are 4 white marbles (represented as W, W, W, W) and 3 black marbles (represented as B, B, B).
Sample space = \(\{W, W, W, W, B, B, B\}\)
In simple words: List each individual marble using its assigned letter according to the total count given in the box.

Exam Tip: When drawing one marble at a time from individual items, list every single item as a separate outcome in the sample space.

Q4. A coin is tossed once. Write the probability of (i) Head (ii) Tail
Answer: Total number of possible outcomes = 2 (\(H\) and \(T\))
(i) Probability of getting a Head = \(\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{2}\)
(ii) Probability of getting a Tail = \(\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{2}\)
In simple words: Since a coin has two sides, both heads and tails have an equal chance of appearing, which is 1 out of 2.

Exam Tip: The sum of probabilities of all possible outcomes in an experiment is always equal to 1.

Q5. A dice is tossed once. What is the probability of (i) 1 (ii) 4 (iii) 6
Answer: Total number of possible outcomes when a die is tossed = 6 (\(1, 2, 3, 4, 5, 6\))
(i) Probability of getting 1 = \(\frac{1}{6}\)
(ii) Probability of getting 4 = \(\frac{1}{6}\)
(iii) Probability of getting 6 = \(\frac{1}{6}\)
In simple words: Every individual number on a fair die has a 1 in 6 chance of appearing.

Exam Tip: Probability is always a fraction where the denominator is the total number of possible outcomes and the numerator is the count of successful outcomes.

Q6. A coin is tossed 50 times in which head turn up 30 times. What is the probability of (i) Head (ii) Tail
Answer: Total number of coin tosses = 50
Number of times head turned up = 30
Number of times tail turned up = \(50 - 30 = 20\)
(i) Probability of getting a Head = \(\frac{30}{50} = \frac{3}{5}\)
(ii) Probability of getting a Tail = \(\frac{20}{50} = \frac{2}{5}\)
In simple words: Based on the experimental results, divide the count of each outcome by the total number of trials.

Exam Tip: Always simplify fractions to their lowest terms (e.g., \(\frac{30}{50}\) becomes \(\frac{3}{5}\)).

Q7. A dice is tossed once, what is the probability of getting 7?
Answer: Total possible outcomes when a die is tossed = 6 (\(1, 2, 3, 4, 5, 6\))
Number of favorable outcomes for getting 7 = 0 (since 7 is not present on a standard die)
Probability of getting 7 = \(\frac{0}{6} = 0\)
In simple words: An impossible event always has a probability of 0.

Exam Tip: The probability of any event can never be less than 0 or greater than 1.

Q8. A box contains 6 marbles marked number 1 to 6. What is the probability of drawing the marble marked 6?
Answer: Total number of marbles in the box = 6
Number of marbles marked 6 = 1
Probability of drawing the marble marked 6 = \(\frac{1}{6}\)
In simple words: There is only one marble marked 6 out of 6 total marbles.

Exam Tip: Identify the target count carefully and place it over the total count.

Q9. A box contains 5 red balls and 9 white balls. What is the probability of drawing (i) white ball (ii) red ball?
Answer: Number of red balls = 5
Number of white balls = 9
Total number of balls = \(5 + 9 = 14$
(i) Probability of drawing a white ball = \(\frac{9}{14}\)
(ii) Probability of drawing a red ball = \(\frac{5}{14}\)
In simple words: Add the red and white balls to find the total, then put the target color count on top.

Exam Tip: Always calculate the total number of items first by adding all given categories together.

Q10. What is the probability of selecting 'S' from the word "LESS"?
Answer: Total number of letters in the word "LESS" = 4
Number of times the letter 'S' appears in "LESS" = 2
Probability of selecting 'S' = \(\frac{2}{4} = \frac{1}{2}\)
In simple words: Count every letter in the word as a separate item, including repetitions.

Exam Tip: Count all individual positions in a word or set, even if letters repeat, when determining total possible selections.