A game consists of tossing a one rupee coin 3 times and noting its outcome each time. Hanif wins if all the tosses give the same result i.e., three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.
Solution and Explanation
The possible outcomes are {HHH, TTT, HHT, HTH, THH, TTH, THT, HTT}
Number of total possible outcomes = 8
Number of favorable outcomes = 2 {i.e., TTT and HHH}
P (Hanif will win the game) =\(\frac{2}{8}=\frac{1}{4}\)
P (Hanif will lose the game) \(=1-\frac{1}{4}=\frac{3}{4}\)
Top Questions on Probability
- Two friends were born in the year 2000. The probability that they have the same birthday is :
- CBSE Class X - 2024
- Mathematics
- Probability
- A box contains cards numbered 6 to 50. A card is drawn at random from the box. The probability that the drawn card has a number which is a perfect square, is :
- CBSE Class X - 2024
- Mathematics
- Probability
- The probability of getting a sum of 8, when two dice are thrown simultaneously, is :
- CBSE Class X - 2024
- Mathematics
- Probability
- A bag contains 4 red, 5 white, and some yellow balls. If the probability of drawing a red ball at random is \(\frac{1}{5}\), then find the probability of drawing a yellow ball at random.
- CBSE Class X - 2024
- Mathematics
- Probability
- Two dice are rolled together. The probability of getting a doublet is:
- CBSE Class X - 2024
- Mathematics
- Probability
Questions Asked in CBSE X exam
- Why was the need for decentralization recognized in the Indian Constitution?
- CBSE Class X - 2024
- Federalism
- An Atal Tinkering Lab (ATL) provides activity-based learning in the identified school across the country where young minds can give shape to their ideas for societal problems. Explain in your own words, how using such a 3D printer can be beneficial to an educational institution, from a design, innovation, and thinking perspective.
- CBSE Class X - 2024
- Prototyping Methods
- You have been given an assignment to deliver a presentation in front of the whole class. What are the key communication skills that you should maintain and why?
- CBSE Class X - 2024
- Communication Skills
- “Hero” video is a prominent and engaging video placed at the top of a website. It’s designed to capture visitor’s attention immediately, typically showcasing key messages, products, or brand stories in a visually appealing and impactful way. Briefly explain about the type of animation medium represented by the “Hero” video. What in your opinion, resulted in such a remarkable impact of the video?
- CBSE Class X - 2024
- Animation
- Explain how “timing” plays a critical role in establishing a character’s nature, personality, mood, and emotion.
- CBSE Class X - 2024
- Animation
Concepts Used:
Probability
Probability is defined as the extent to which an event is likely to happen. It is measured by the ratio of the favorable outcome to the total number of possible outcomes.
The definitions of some important terms related to probability are given below:
Sample space
The set of possible results or outcomes in a trial is referred to as the sample space. For instance, when we flip a coin, the possible outcomes are heads or tails. On the other hand, when we roll a single die, the possible outcomes are 1, 2, 3, 4, 5, 6.
Sample point
In a sample space, a sample point is one of the possible results. For instance, when using a deck of cards, as an outcome, a sample point would be the ace of spades or the queen of hearts.
Experiment
When the results of a series of actions are always uncertain, this is referred to as a trial or an experiment. For Instance, choosing a card from a deck, tossing a coin, or rolling a die, the results are uncertain.
Event
An event is a single outcome that happens as a result of a trial or experiment. For instance, getting a three on a die or an eight of clubs when selecting a card from a deck are happenings of certain events.
Outcome
A possible outcome of a trial or experiment is referred to as a result of an outcome. For instance, tossing a coin could result in heads or tails. Here the possible outcomes are heads or tails. While the possible outcomes of dice thrown are 1, 2, 3, 4, 5, or 6.