Answer
Verified
479.1k+ views
The given question is related to probability. Try to recall the formulae related to probability of simultaneous occurrence of independent events.
Complete step-by-step answer:
We are given the case of a coin toss game. We know, during a coin toss there are only two possible outcomes, i.e. heads or tails. The probability of occurrence of head in a single toss is given as $P(H)=\dfrac{1}{2}$ and similarly, the probability of occurrence of a tail in a single toss is given as $P(T)=\dfrac{1}{2}$. In case of three tosses, the possible outcomes are as follows:
No heads: (T, T, T)
One head: (T, T, H), (T, H, T), (H, T, T)
Two heads: (H, H, T), (H, T, H), (T, H, H)
Three heads: (H, H, H)
Now, total number of possible outcomes is equal to $8$, { (H, H, H), (T, T, H), (T, H, T), (H, T, T), (H, H, T), (H, T, H), (T, H, H), (T, T, T) }. We are asked to find the probability that Hanif will lose the game. It is given that Hanif will lose the game if the outcomes of all the tosses are not the same, i.e. if the outcomes of all tosses are not heads or tails. The number of all such cases is $6$, { (T, T, H), (T, H, T), (H, T, T), (H, H, T), (H, T, H), (T, H, H) }.
Now, we know, probability $P=\dfrac{Number\,of\,favorable\,outcomes}{Number\,of\,total\,possible\,outcomes}$.
So, the probability that Hanif will lose the game is given as \[P=\dfrac{6}{8}=\dfrac{3}{4}\].
Note: While calculating probability, make sure to check every possible outcome. Generally, students miss one or two possible outcomes, because of which the value of probability changes and the wrong answer is obtained.
Complete step-by-step answer:
We are given the case of a coin toss game. We know, during a coin toss there are only two possible outcomes, i.e. heads or tails. The probability of occurrence of head in a single toss is given as $P(H)=\dfrac{1}{2}$ and similarly, the probability of occurrence of a tail in a single toss is given as $P(T)=\dfrac{1}{2}$. In case of three tosses, the possible outcomes are as follows:
No heads: (T, T, T)
One head: (T, T, H), (T, H, T), (H, T, T)
Two heads: (H, H, T), (H, T, H), (T, H, H)
Three heads: (H, H, H)
Now, total number of possible outcomes is equal to $8$, { (H, H, H), (T, T, H), (T, H, T), (H, T, T), (H, H, T), (H, T, H), (T, H, H), (T, T, T) }. We are asked to find the probability that Hanif will lose the game. It is given that Hanif will lose the game if the outcomes of all the tosses are not the same, i.e. if the outcomes of all tosses are not heads or tails. The number of all such cases is $6$, { (T, T, H), (T, H, T), (H, T, T), (H, H, T), (H, T, H), (T, H, H) }.
Now, we know, probability $P=\dfrac{Number\,of\,favorable\,outcomes}{Number\,of\,total\,possible\,outcomes}$.
So, the probability that Hanif will lose the game is given as \[P=\dfrac{6}{8}=\dfrac{3}{4}\].
Note: While calculating probability, make sure to check every possible outcome. Generally, students miss one or two possible outcomes, because of which the value of probability changes and the wrong answer is obtained.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Change the following sentences into negative and interrogative class 10 english CBSE
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE