State true or false.In a game, the entry fee is Rs 5. The game consists of tossing a coin 3 times. If one or two heads show, Sweta gets her entry fee back. If she throws 3 heads, she receives double the entry fees. Otherwise, she will lose. For tossing a coin three times, the probability that she just gets her entry fee is 34.

Question

Accepted Answer

Given that in a game, the game consists of tossing a coin 3 times. Let us assume that P(D) is the probability of an event “D”, n(S) is the total number of events in the sample space and n(D) is the number of favorable outcomes.The total number of possible outcomes are

HHH
   
  ,

TTT
   
  ,

HTT
   
  ,

THT
   
  ,

TTH
   
  ,

THH
   
  ,

HTH
   
  ,

HHT
   
   . So,

n
    S
   =8
   . Let D be the event that Sweta gets her entry fee back that means Sweta gets heads one or two times. So,

n
    D
   =6
   . The probability is,

P
      D
     =
      
       Number of favourable outcomes
      
       Total number of outcomes

P
      D
     =
      
       n
        D

n
        S

P
      D
     =
      6
      8

P
      D
     =
      3
      4

Therefore, 1 is the correct option and the statement is true.

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