# Two unbiased coins are tossed simultaneously. Find the probability of getting

i. two heads

ii. one tail

iii. at least one tail

iv. at most one tail

v. no tail

Last updated date: 17th Mar 2023

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Answer

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Hint- In order to solve such type of question we must use formula Probability \[\left( {\text{P}} \right){\text{ = }}\dfrac{{{\text{Favourable number of cases}}}}{{{\text{Total number of cases}}}}\] , along with proper understanding of favourable cases and total cases.

Complete step-by-step answer:

If two unbiased coins are tossed simultaneously, then the total number of possible outcomes may be either.

1.both head HH

2.one head and one tail (HT, TH)

3.Both tail (TT)

So here total number of possible cases = 4

(i) two heads

a favourable outcome for two heads is HH.

No. of favourable outcomes = 1

total number of possible cases = 4

As we know that Probability \[\left( {\text{P}} \right){\text{ = }}\dfrac{{{\text{Favourable number of cases}}}}{{{\text{Total number of cases}}}}\]

Probability (two heads) =$\dfrac{1}{4}$

(ii) favourable outcomes for one tail are TH, HT.

No. of favourable outcomes = 2

total number of possible cases = 4

As we know that Probability \[\left( {\text{P}} \right){\text{ = }}\dfrac{{{\text{Favourable number of cases}}}}{{{\text{Total number of cases}}}}\]

Probability(one tail) = $\dfrac{2}{4}{\text{ = }}\dfrac{1}{2}$

(iii) favourable outcomes for at least one tail are TH, HT, TT.

No. of favourable outcomes = 3

total number of possible cases = 4

As we know that Probability \[\left( {\text{P}} \right){\text{ = }}\dfrac{{{\text{Favourable number of cases}}}}{{{\text{Total number of cases}}}}\]

Probability (at least one tail) = $\dfrac{3}{4}$

(iv) Favourable outcomes for at least one head are TH, HT, HH.

No. of favourable outcomes = 3

total number of possible cases = 4

As we know that Probability \[\left( {\text{P}} \right){\text{ = }}\dfrac{{{\text{Favourable number of cases}}}}{{{\text{Total number of cases}}}}\]

Probability (at least one head) = $\dfrac{3}{4}$

(v) favourable outcomes for no tail means not a single head is HH.

No. of favourable outcomes = 1

total number of possible cases = 4

As we know that Probability \[\left( {\text{P}} \right){\text{ = }}\dfrac{{{\text{Favourable number of cases}}}}{{{\text{Total number of cases}}}}\]

Probability(no tail) = $\dfrac{1}{4}$

NOTE- In Such Types of Question first find out the total numbers of possible outcomes then find out the number of favourable cases, then divide them using the formula which stated above, we will get the required answer.

Complete step-by-step answer:

If two unbiased coins are tossed simultaneously, then the total number of possible outcomes may be either.

1.both head HH

2.one head and one tail (HT, TH)

3.Both tail (TT)

So here total number of possible cases = 4

(i) two heads

a favourable outcome for two heads is HH.

No. of favourable outcomes = 1

total number of possible cases = 4

As we know that Probability \[\left( {\text{P}} \right){\text{ = }}\dfrac{{{\text{Favourable number of cases}}}}{{{\text{Total number of cases}}}}\]

Probability (two heads) =$\dfrac{1}{4}$

(ii) favourable outcomes for one tail are TH, HT.

No. of favourable outcomes = 2

total number of possible cases = 4

As we know that Probability \[\left( {\text{P}} \right){\text{ = }}\dfrac{{{\text{Favourable number of cases}}}}{{{\text{Total number of cases}}}}\]

Probability(one tail) = $\dfrac{2}{4}{\text{ = }}\dfrac{1}{2}$

(iii) favourable outcomes for at least one tail are TH, HT, TT.

No. of favourable outcomes = 3

total number of possible cases = 4

As we know that Probability \[\left( {\text{P}} \right){\text{ = }}\dfrac{{{\text{Favourable number of cases}}}}{{{\text{Total number of cases}}}}\]

Probability (at least one tail) = $\dfrac{3}{4}$

(iv) Favourable outcomes for at least one head are TH, HT, HH.

No. of favourable outcomes = 3

total number of possible cases = 4

As we know that Probability \[\left( {\text{P}} \right){\text{ = }}\dfrac{{{\text{Favourable number of cases}}}}{{{\text{Total number of cases}}}}\]

Probability (at least one head) = $\dfrac{3}{4}$

(v) favourable outcomes for no tail means not a single head is HH.

No. of favourable outcomes = 1

total number of possible cases = 4

As we know that Probability \[\left( {\text{P}} \right){\text{ = }}\dfrac{{{\text{Favourable number of cases}}}}{{{\text{Total number of cases}}}}\]

Probability(no tail) = $\dfrac{1}{4}$

NOTE- In Such Types of Question first find out the total numbers of possible outcomes then find out the number of favourable cases, then divide them using the formula which stated above, we will get the required answer.

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