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Q.

A game consists of tossing a one rupee coin 3 times and noting its outcome each time. Hanif wins if all the tosses give the same result, i.e., three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.


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a

1 2  

b

3 4  

c

1 3  

d

1 4   

answer is B.

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Detailed Solution

It is given that a game consists of tossing a one rupee coin 3 times and noting its outcome each time.
Total number of outcomes when coin tossed three times are HHH, HHT, HTT, TTT, TTH, THH, THT, HTH.
Thus, the total number of outcomes are 8.
Outcomes with the tosses give the same results are HHH, TTT.
Hence, the outcomes with different results are 8-2 = 6.
Hence, the number of favourable outcomes with different results on coins are 6.
Now, the probability is given by,
  Probability =  Number of favorable outcomes Total number of outcomes  
Probability of Hanif will lose the game is,
Probability =  6 8 Probability = 3 4  
Hence, the probability of Hanif will lose the game is 3 4  .
Therefore, the correct answer is option (2).
 
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