# Three unbiased coins are tossed together. Find the probability of getting two heads.

Last updated date: 28th Mar 2023

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Hint- Here, we will be proceeding by analyzing all the possible outcomes when three unbiased coins are tossed together.

Given, three unbiased coins are tossed together.

The possible cases or outcomes which will arise are given by

\[{\text{(H,H,H),(H,H,T),(H,T,H),(T,H,H),(H,T,T),(T,H,T),(T,T,H)}},(T,T,T)\] where H represents head occurring and T represents tail occurring.

As we know that the general formula for probability is given as

\[{\text{Probability of occurrence of an event}} = \dfrac{{{\text{Total number of favorable outcomes}}}}{{{\text{Total number of possible outcomes}}}}\]

Here, the favorable event is the occurrence of two heads when three coins are tossed together.

Therefore, favorable cases where two heads occur when three coins are tossed together are \[{\text{(H,H,T),(H,T,H),(T,H,H)}}\].

Clearly, Total number of favorable outcomes\[ = 3\] and Total number of possible outcomes\[ = 8\].

Therefore, Probability of occurrence of two heads when three unbiased coins are tossed together\[ = \dfrac{3}{8}\].

Note- These types of problems are solved with the help of the general formula of probability in which the favorable event is referred to as the event of getting two heads when three unbiased coins are tossed together. Here, all the possible cases which can occur need to be considered.

Given, three unbiased coins are tossed together.

The possible cases or outcomes which will arise are given by

\[{\text{(H,H,H),(H,H,T),(H,T,H),(T,H,H),(H,T,T),(T,H,T),(T,T,H)}},(T,T,T)\] where H represents head occurring and T represents tail occurring.

As we know that the general formula for probability is given as

\[{\text{Probability of occurrence of an event}} = \dfrac{{{\text{Total number of favorable outcomes}}}}{{{\text{Total number of possible outcomes}}}}\]

Here, the favorable event is the occurrence of two heads when three coins are tossed together.

Therefore, favorable cases where two heads occur when three coins are tossed together are \[{\text{(H,H,T),(H,T,H),(T,H,H)}}\].

Clearly, Total number of favorable outcomes\[ = 3\] and Total number of possible outcomes\[ = 8\].

Therefore, Probability of occurrence of two heads when three unbiased coins are tossed together\[ = \dfrac{3}{8}\].

Note- These types of problems are solved with the help of the general formula of probability in which the favorable event is referred to as the event of getting two heads when three unbiased coins are tossed together. Here, all the possible cases which can occur need to be considered.

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