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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Solution

Sample space $= {H H H, H H T, H T H, H T T, T H H, T H T, T T H, T T T}$
Outcomes when he does not choose $3$ heads or $3$ tails $= {H H T, H T H, H T T, T H H, T H T, T T H}$

Probability of losing $= \frac{6}{8} = \frac{3}{4}$

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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.

Sample space ={HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}Outcomes when he does not choose 3 heads or 3 tails ={HHT,HTH,HTT,THH,THT,TTH}Probability of losing =68=34

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.

Sample space $= {H H H, H H T, H T H, H T T, T H H, T H T, T T H, T T T}$
Outcomes when he does not choose $3$ heads or $3$ tails $= {H H T, H T H, H T T, T H H, T H T, T T H}$

Probability of losing $= \frac{6}{8} = \frac{3}{4}$