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Home » An experiment consists of tossing a coin and then throwing it second time if a head occurs. If a tail occurs on the first toss, then a die is rolled once. Find the sample space.
An experiment consists of tossing a coin and then throwing it second time if a head occurs. If a tail occurs on the first toss, then a die is rolled once. Find the sample space.
CBSE | Class 11 | Exercise 16.1 | Maths | NCERT | Probability
An experiment consists of tossing a coin and then throwing it second time if a head occurs. If a tail occurs on the first toss, then a die is rolled once. Find the sample space.

Assume that 1,2,3,4,5 and 6 are the possible outcomes when the die is thrown.

When a coin is tossed then the possible outcomes can be either Head (H) or Tail (T).

Consider,

Case 1: Head is encountered

Sample space {{S}_{1~}}=\text{ }\left\{ HT,\text{ }HH \right\}

Case 2: Tail is encountered

Sample Space {{S}_{2~}}=\text{ }\left\{ \left( T,1 \right),\text{ }\left( T,2 \right),\text{ }\left( T,3 \right),\text{ }\left( T,4 \right),\text{ }\left( T,5 \right),\text{ }\left( T,6 \right) \right\}

Therefore, the Sample space of the event is

S\text{ }=\text{ }\left\{ \left( HT \right),\text{ }\left( HH \right),\text{ }\left( T1 \right),\text{ }\left( T2 \right),\text{ }\left( T3 \right),\text{ }\left( T4 \right),\text{ }\left( T5 \right),\text{ }\left( T6 \right) \right\}

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