Answer
Verified
416.1k+ 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
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE
Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE
What are the possible quantum number for the last outermost class 11 chemistry CBSE
Is C2 paramagnetic or diamagnetic class 11 chemistry CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Select the correct plural noun from the given singular class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
The sum of three consecutive multiples of 11 is 363 class 7 maths CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
How many squares are there in a chess board A 1296 class 11 maths CBSE