Question

If three coins are tossed simultaneously then the probability of getting at least two tails .
A. \[\dfrac{1}{8}\]
B. \[\dfrac{1}{4}\]
C. \[\dfrac{1}{2}\]
D. None of these

Answer 1

Hint: If three coins are tossed simultaneously then the sample space will be S \[ = \] { HHH , TTT , HHT , HTH , THH , TTH , THT , HTT } . If the event occurred , two tails will be the favorable outcome for the required question . To find the probability of an event we use a formula \[ = \dfrac{{no.{\text{ of favorable events}}}}{{Total{\text{ no}}{\text{. of outcomes}}}}\] .

Complete step by step answer:
Given : Let \[E\] be the event that occurred .
 Number of coins tossed simultaneously \[ = 3\] .
Number of possible outcomes can be calculated by using a formula \[ = {2^n}\] where \[n\] represents the number of outcomes for a given coin .
Therefore , the total number of outcomes for three coins will be \[ = {2^3}\] .
Total outcomes will be \[ = 8\] .
For favorable outcomes, count the number of outcomes from the sample space of events that occurred with at least two heads which comes out to be \[ = 4\] .
Now , to find the probability we use the formula \[ = \dfrac{{no.{\text{ of favorable events}}}}{{Total{\text{ no}}{\text{. of outcomes}}}}\] ,
Therefore , the probability for the event \[E\] will be \[P(E)\] which is
\[ = \dfrac{4}{8}\] , on solving we get
\[ = \dfrac{1}{2}\] .

So, the correct answer is “Option C”.

Note: Always try to find the sample space for the event as it will ease out the question. Moreover , the event should be defined as \[E\] and if other events are also there then also defined as \[{E_1}\] , \[{E_2}\] , ….
In your solution . For larger sample space use permutation and combination but check whether the event is repeating or not .