Question

Two coins are tossed simultaneously. Write the samples pace S and number of sample points n(S). A is the event of getting no head. Write the event of A in set notation and find n(A).

Answer 1

Hint: To solve the question, we have to analyse all the possible outcomes when the coin is tossed 2 times and calculate the number of cases which result in event A.

Complete step by step answer:
Given
The number of times the coin tossed = 2

The obtained outcomes are given by the following possible ways,

The possible outcomes of 2 heads (H H) = 1

The possible outcomes of 1 head and 1 tail are (H T, T H) = 2

The possible outcomes of 2 tails (T T) = 1

Where H, T are heads, tails of a coin respectively.

Thus, the total number of outcomes when the coin is tossed 3 times = 1 + 2 + 1 = 4

The sample space of two coin tossed = All the possible outcomes

Thus, the sample space \[S=\left\{ \left( H,H \right),\left( H,T \right),\left( T,H \right),\left( T,T \right) \right\}\]

The number of sample points in sample space = n(S) = 4

The event of A occurs when the no head is seen in the tosses. This condition is seen in the outcome of 2 tails.

Thus, only 1 case is obtained for the event of A.

Thus, the set notation of \[A=\left\{ \left( T,T \right) \right\}\].

The number of sample points in event A = n(A) = 1

Note: The possibility of mistake can happen at analysing the outcomes when 2 coins are tossed simultaneously. The alternative quick method of solving can be that the number of outcomes will be equal to \[=2\times 2=4\] since there can be only cases of heads or tails and the coin is tossed 2 times. Thus, we can obtain that case of event A is 1.