GSEB Class 8 Maths Solutions Chapter 5 Data Handling Exercise 5.3

Question 1. List the outcomes you can see in these experiments?
(a) Spinning a wheel
(b) Tossing two coins together

Answer:
(a) The outcomes for spinning the given wheel are: A, B, C, or D.
(b) The outcomes from tossing two coins together are: HT, HH, TH, TT. Here, HT means Head on the first coin and Tail on the second coin, and so forth.
In simple words: When you spin the wheel, you can land on A, B, C, or D. If you toss two coins, you can get a Head and a Tail, two Heads, a Tail and a Head, or two Tails.

Exam Tip: Always list all possible unique outcomes for each event to ensure full coverage.

Question 2. When a die is thrown, list the outcome of an event of getting:
(i) (a) a prime number
(b) not a prime number
(ii) (a) a number greater than 5
(b) a number not greater than 5
Answer:
Possible outcomes from throwing a die are: 1, 2, 3, 4, 5, or 6. Among these, the prime numbers are 2, 3, and 5.
(i) (a) The outcomes for getting a prime number are: 2, 3, or 5.
(b) The outcomes for getting not a prime number are: 1, 4, or 6.
(ii) (a) The outcome for getting a number greater than 5 is 6.
(b) The outcomes for getting a number not greater than 5 are: 1, 2, 3, 4, or 5.
In simple words: When you roll a dice, you can get numbers from 1 to 6. Prime numbers are 2, 3, 5. Numbers that are not prime are 1, 4, 6. The only number bigger than 5 is 6. Numbers not bigger than 5 are 1, 2, 3, 4, 5.

Exam Tip: Remember that 1 is neither prime nor composite. Clearly distinguish between "greater than" and "greater than or equal to".

Question 3. Find:
(a) The probability of the pointer stopping on D in a spinning wheel
(b) The probability of getting an ace from a well-shuffled deck of 52 playing cards?
(c) The probability of getting a red apple (See figure below)

Answer:
(a) The spinning wheel contains 5 sectors in total, including A, B, C, and D. Since there is only one sector with D, the number of possible outcomes for D is 1. The total number of equally likely outcomes is 5. Therefore, the probability of getting D is \( \frac{1}{5} \).
(b) The total number of possible outcomes in a standard deck of 52 playing cards is 52. There are 4 aces in a pack of 52 cards, so one ace can be drawn in 4 different ways. Therefore, the probability of getting an ace is \( \frac{4}{52} = \frac{1}{13} \).
(c) There are 7 apples in total. Since there are 4 red apples, a red apple can be obtained in 4 ways. Thus, the probability of getting a red apple is \( \frac{4}{7} \).
In simple words: (a) The wheel has 5 spots, and only one is D, so you have a 1 in 5 chance to land on D. (b) A deck has 52 cards, and 4 of them are aces, so your chance of picking an ace is 4 out of 52, which simplifies to 1 in 13. (c) There are 7 apples total, and 4 are red, so you have a 4 in 7 chance of picking a red apple.

Exam Tip: Remember that probability is always expressed as a fraction: (favorable outcomes) / (total possible outcomes). Always simplify fractions to their lowest terms.

Question 4. Numbers 1 to 10 are written on ten separate slips (one number on one slip), kept in a box and mixed well. One slip is chosen from the box without looking into it. What is the probability of:
1. getting a number 6?
2. getting a number less than 6?
3. getting a number greater than 6?
4. getting a 1-digit number?
Answer:
There are 10 slips in the box, each with a number from 1 to 10. Any slip can be chosen at a time. The total number of outcomes is 10.
1. You can get a slip with the number '6' only once. So, the number of favorable outcomes is 1. Thus, the probability of getting the number 6 is \( \frac{1}{10} \).
2. There are five numbers (1, 2, 3, 4, and 5) that are less than 6. The favorable outcomes are 5. Thus, the probability of getting a number less than six is \( \frac{5}{10} = \frac{1}{2} \).
3. There are 4 numbers (7, 8, 9, 10) that are greater than six. The favorable outcomes are 4. Thus, the probability of getting a number greater than six is \( \frac{4}{10} = \frac{2}{5} \).
4. There are nine one-digit numbers (1, 2, 3, 4, 5, 6, 7, 8, and 9). The favorable outcomes are 9. Thus, the probability of getting a one-digit number is \( \frac{9}{10} \).
In simple words: There are 10 slips. 1. You can only pick '6' once, so the chance is 1 out of 10. 2. Numbers smaller than 6 are five (1,2,3,4,5), so the chance is 5 out of 10, or 1/2. 3. Numbers bigger than 6 are four (7,8,9,10), so the chance is 4 out of 10, or 2/5. 4. Nine numbers (1-9) have only one digit, so the chance is 9 out of 10.

Exam Tip: Carefully identify the total possible outcomes and the specific favorable outcomes for each part of the question. Remember to simplify fractions where possible.

Question 5. If you have a spinning wheel with 3 green sectors, 1 blue sector and 1 red sector, what is the probability of getting a green sector? What is the probability of getting a non-blue sector?
Answer:
There are 5 sectors in total on the wheel (3 green + 1 blue + 1 red). So, there are 5 possible outcomes.
Since there are 3 green sectors, the number of favorable outcomes for getting a green sector is 3. Therefore, the probability of getting a green sector is \( \frac{3}{5} \).
For a non-blue sector, there are 4 such sectors (3 green + 1 red). The favorable outcomes are 4. Thus, the probability of getting a 'non-blue' sector is \( \frac{4}{5} \).
In simple words: There are 5 total parts on the wheel. Three are green, so the chance of landing on green is 3 out of 5. Four parts are not blue (the three green and one red), so the chance of landing on a non-blue part is 4 out of 5.

Exam Tip: For "non-X" probability, calculate total outcomes minus outcomes for "X" to find favorable outcomes.

Question 6. Find the probabilities of the events given in Question 2?
Answer:
When a die is thrown, there are 6 possible outcomes in total (1, 2, 3, 4, 5, 6).
1. Since there are 3 prime numbers (2, 3, and 5) from the possible outcomes, the number of favorable outcomes is 3. Thus, the probability of getting a prime number is \( \frac{3}{6} = \frac{1}{2} \).
2. Since there are 3 non-prime numbers (1, 4, and 6) from the possible outcomes, the number of favorable outcomes is 3. Thus, the probability of getting a non-prime number is \( \frac{3}{6} = \frac{1}{2} \).
3. Since there is only 1 number greater than 5 (which is 6), the number of favorable outcomes is 1. Thus, the probability of a number greater than 5 is \( \frac{1}{6} \).
4. Since there are 5 numbers that are not greater than 5 (1, 2, 3, 4, and 5), the number of favorable outcomes is 5. Thus, the probability of a number which is not greater than 5 is \( \frac{5}{6} \).
In simple words: For a rolled die, there are 6 possible results. 1. Three numbers are prime (2,3,5), so the chance is 3/6 or 1/2. 2. Three numbers are not prime (1,4,6), so the chance is 3/6 or 1/2. 3. Only one number is greater than 5 (which is 6), so the chance is 1/6. 4. Five numbers are not greater than 5 (1,2,3,4,5), so the chance is 5/6.

Exam Tip: Ensure you understand how each part of a previous question (like Question 2) translates into a probability calculation in a subsequent question.