Examine each of the following statements and comment: If two coins are tossed at the same time, there are 3 possible outcomes - two heads, two tails, or one of each. Therefore, for each outcome, the probability of occurrence is $ \frac{1}{3}. $
Given:
If two coins are tossed at the same time, there are 3 possible outcomes - two heads, two tails, or one of each. Therefore, for each outcome, the probability of occurrence is \( \frac{1}{3}. \)
To do:
We have to find whether the given statement is true or false.
Solution:
When two coins are tossed simultaneously, the total possible outcomes are HH, HT, TH and TT.
This implies,
The total number of possible outcomes $n=4$.
We know that,
Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$
Therefore,
Probability of getting two heads $=\frac{1}{4}$
Probability of getting two tails $=\frac{1}{4}$
Probability of getting one head and one tail $=\frac{2}{4}=\frac{1}{2}$
Therefore, the given statement is false.
Related Articles
- Which of the following arguments are correct and which are not correct? Give reasons for your answer.(i) If two coins are tossed simultaneously there are three possible outcomes- two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is $\frac{1}{3}$.(ii) If a die is thrown, there are two possible outcomes- an odd number or an even number. Therefore, the probability of getting an odd number is $\frac{1}{2}$.
- Examine each of the following statements and comment: If a die is thrown once, there are two possible outcomes -an odd number or an even number. Therefore, the probability of obtaining an odd number is \( \frac{1}{2} \) and the probability of obtaining an even number is \( \frac{1}{2} . \)
- Three different coins are tossed together. Find the probability of getting: $( i)$ exactly two heads $( ii)$ at least two heads $( iii)$ at least two tails.
- If three coins are tossed simultaneously, then write their outcomes.$( a)$. All possible outcomes.$( b)$. Number of possible outcomes.$( c)$. Find the probability of getting at least one head.$( d)$. Find the Probability of getting at most two heads.$( e)$. Find the Probability of getting no tails.
- Three coins are tossed together. Find the probability of getting at most two heads.
- Three coins are tossed together. Find the probability of getting exactly two heads.
- Two coins are tossed simultaneously 500 times with the following frequencies of differentoutcomes:Two heads : 95 timesOne tail : 290 timesNo head: 115 timesFind the probability of occurrence of each of these events.
- List the possible outcomes when two coins tossed together.
- Find the probability of getting exactly one head when two coins are tossed.
- Make the sample space of tossing two coins simultaneously and find the probability of:1. Exactly two heads2. At least one head3. At least one tail4. At most two tails
- Two dice, one blue and one grey, are thrown at the same time.A student argues that-there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability $\frac{1}{11}$. Do you agree with this argument? Justify your answer.
- Three coins are tossed together. Find the probability of getting no tails.
- Which of the following arguments are correct and which are not correct? Give reasons for your answer.If a die is thrown, there are two possible outcomes- an odd number or an even number. Therefore, the probability of getting an odd number is $\frac{1}{2}$.
- Write two solutions for each of the following equations$\frac{2}{3} x - y = 4$
- 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.
Kickstart Your Career
Get certified by completing the course
Get Started
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies