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Solution


Q.

Three unbiased coins are tossed together. Then:

(i) the probability of getting exactly 2 heads is 1/2.

(ii) the probability of getting atleast one head is 7/8.

(iii) the probability of getting atmost 2 tails is 7/8.

(iv) the probability of getting exactly one tail is 3/8.

 

Choose correct option from the following:
1 (i), (ii) and (iii)  
2 (i), (iii) and (iv)  
3 (ii), (iii) and (iv)  
4 (i) and (iii)  

Ans.

(3)

When three unbiased coins are tossed together,
Possible outcomes are HHH, HHT, HTH, THH, HTT, THT, TTH, TTT.
The number of all possible outcomes is 8 ⇒ n(S) = 8

(i) The outcomes favourable to the event E ‘exactly two heads’ are HHT, HTH, THH i.e.,  n(E)=3 P(E)= Probability of getting exactly 2 heads =3/8, statement (i) is not true.

(ii) The outcomes favourable to the event F ‘atleast one head’ are HHH, HHT, HTH, THH, HTT, THT, TTH i.e., n(F)=7

P(F)=Probability of getting atleast one head =7/8, statement (ii) is true.

(iii) The outcomes favourable to the event G ‘atmost two tails’ are HHH, HHT, HTH, THH, HTT, THT, TTH i.e., n(G)=7

P(G)=Probability of getting atmost 2 tails =7/8, statement (iii) is true.

(iv) The outcomes favourable to the event H ‘exactly one tail’ are HHT, HTH, THH i.e., n(H)=3

P(H)=Probability of getting exactly one tail =3/8, statement (iv) is true.

So, option (ii), (iii) and (iv) are correct.