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Class 10 Maths Chapter 14 HOTS Questions - Probability
1. A bag-I contains four cards numbered 1, 3, 5 and 7 respectively. Another bag-II contains three cards numbered 2, 4 and 6 respectively. A card is drawn at random from each bag. Find the probability that the sum of two cards drawn is 9.
All outcomes = 12 ⇒ |
2. A bag contains 7 white, 3 red and 4 black balls. A ball is drawn at random. Find the probability that it is a red or a black ball.
| Hint: Total number of possible outcomes = 7 + 3 + 4 = 14. Out of 14 possible outcomes, there are 7 favourable outcomes (3 red and 4 black) i.e. there are 7 balls that are either red or black. ∴ Required probability = P(a red or a black ball) = (7/14)= (1/2) |
3. In a single throw of two dice, find the probability of getting a total of 8.
∴ Favourable outcomes are : (2, 6), (3, 5), (4, 4), (5, 3), (6, 2) i.e. 5 outcomes are favourable. |
4. One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting a face card.
| Hint: 52 cards are divided into 4 suits of 13 cards each. Kings, queen and jacks are called face-cards. ∴ Total number of face cards = 3 × 4 = 12 ∴ Favourable outcomes = 12 ⇒ Required probability = (12/52)= (3/13) |
5. Two unbiased coins are tossed once. What is the probability of getting exactly one head?
| Hint: In a throw of two coins, the total number of possible outcomes = 22 = 4 [namely : (H, H), (H, T), (T, H) and (T, T)]. For the event of getting exactly one head (i.e. no tail). ⇒ Favourable outcomes are (H, T) and (T, H) i.e., 2 ⇒ Required probability = (2/4)= (1/2) |
FAQs on Class 10 Maths Chapter 14 HOTS Questions - Probability
| 1. What is probability and how is it related to mathematics? |  |
Ans. Probability is a branch of mathematics that deals with the likelihood of an event occurring. It is used to quantify the uncertainty or randomness of an event. By using mathematical formulas and calculations, probability helps us understand the chances of an event happening and make informed decisions based on those probabilities.
| 2. How is probability calculated for an event? | |
Ans. Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This is expressed as a fraction, decimal, or percentage. For example, if you want to calculate the probability of rolling a 6 on a fair six-sided die, there is only one favorable outcome (rolling a 6) out of six possible outcomes (numbers 1 to 6). Therefore, the probability would be 1/6 or approximately 0.167 (16.7%).
| 3. What is the difference between theoretical probability and experimental probability? | |
Ans. Theoretical probability is based on mathematical calculations and predictions. It is determined by analyzing the possible outcomes and their likelihood in a given situation. On the other hand, experimental probability is based on actual observations and data collected from conducting experiments or trials. It involves performing the event multiple times and recording the outcomes to determine the probability. Theoretical probability provides an expected value, while experimental probability provides an observed value based on real-world data.
| 4. How can probability be used in everyday life? | |
Ans. Probability has various applications in everyday life. It helps us make decisions by considering the likelihood of different outcomes. For example, when choosing between different routes to reach a destination, we can consider the probability of encountering heavy traffic on each route and choose the one with the lowest probability. Probability is also used in insurance, gambling, weather forecasting, sports predictions, and financial investments. It helps in understanding and managing risks and uncertainties.
| 5. What are the fundamental principles of probability? | |
Ans. The fundamental principles of probability include the addition rule, multiplication rule, and complement rule. The addition rule states that the probability of two mutually exclusive events occurring is the sum of their individual probabilities. The multiplication rule states that the probability of two independent events occurring together is the product of their individual probabilities. The complement rule states that the probability of an event not occurring is 1 minus the probability of the event occurring. These principles form the basis for calculating probabilities in various scenarios.
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