A coin is tossed. If a head comes up, a die is thrown, but if a tail c

1.	A coin is tossed. If a head comes up, a die is thrown, but if a tail comes up, the coin is tossed again. Find the probability of obtaining (i) two tails (ii) a head and the number 6 (iii) a head and an even number.
Answer» Given : let H be head, and T be tails where as 1,2,3,4,5,6 be the numbers on the dice which are thrown when a head comes up or else coin is tossed again if its tail. According to the question , sample space S = {(TH),(TT) ,(H1),(H2),(H3),(H4),(H5),(H6)} To Find: (i) the probability of obtaining two tails From sample space, it is clear that the probability of obtaining two tails is\(\frac{1}{8}\) i.e., {TT} with total no of elements in sample space as 8. (ii) the probability of obtaining a head and the number 6 From sample space, it is clear that the probability of obtaining a head and the number 6 is\(\frac{1}{8}\) i.e., {H6} with total no of elements in sample space as 8. (iii) the probability of obtaining a head and an even number From sample space, it is clear that the probability of obtaining a head and an even number is\(\frac{3}{8}\) i.e, {H2,H4,H6} with total no of elements in sample space as 8.

A coin is tossed. If a head comes up, a die is thrown, but if a tail comes up, the coin is tossed again. Find the probability of obtaining (i) two tails (ii) a head and the number 6 (iii) a head and an even number.

Answer»

Given : let H be head, and T be tails where as 1,2,3,4,5,6

be the numbers on the dice which are thrown when a head comes up or else coin is tossed again if its tail.

According to the question ,

sample space S = {(TH),(TT) ,(H1),(H2),(H3),(H4),(H5),(H6)}

To Find:

(i) the probability of obtaining two tails

From sample space, it is clear that the probability of obtaining two tails is\(\frac{1}{8}\)

i.e., {TT} with total no of elements in sample space as 8.

(ii) the probability of obtaining a head and the number 6

From sample space, it is clear that the probability of obtaining a head and the number 6 is\(\frac{1}{8}\)

i.e., {H6} with total no of elements in sample space as 8.

(iii) the probability of obtaining a head and an even number

From sample space, it is clear that the probability of obtaining a head and an even number is\(\frac{3}{8}\)

i.e, {H2,H4,H6} with total no of elements in sample space as 8.