Question

The entrance fee for a game is Rs 5. In this game 1 coin is tossed thrice. If Shweta tosses the coin and gets one or two heads, she gets back her fee paid. If she gets three heads, she gets double of her entry fee. Otherwise she losses amount she has paid. When a coin tossed thrice find the probability that : 

(i) She will loss the entry fee.

(ii) She will get the double of entry fee.

(iii) She will only get back her entry fee.

Answer 1

In the game 1 coin is tossed thrice, 

so all possible outcomes are

HHH, HHT, HTH, THH, THT, HTT, TTH, TTT.

∴ Total number of all possible outcomes = 8.

(i) The entry fee in the game is Rs 5, if three tails are obtained, Shweta will loss her entry fee.

Let the event of getting three heads be (A).

The favourable outcomes of event A = (TTT)

∴ The number of favourable events of (A) = 1.

P(A) = \(\frac { 1 }{ 8 }\)

(ii) If Shweta gets three heads, she will get double of entry fee.

Let the event of occurring 3 heads be (B).

∴ The favourable outcomes of event B = (HHH)

The number of favourable outcomes of (B) = 1

⇒ P(B) = \(\frac { 1 }{ 8 }\)

(iii) If she gets one or two heads, she will get back her enty fee.

Let the event ofoccuring one or two heads be (C).

The favourable outcomes of event C

 = HHT, HTH, THH, THT, HTT, TTH.

∴ The number of favourable outcomes of (C) = 6

⇒ P(C) = \(\frac { 6 }{ 8 }\) = \(\frac { 3 }{ 4 }\)