Question

A coin is tossed and a die is rolled. What is the probability that the coin shows heads and the die shows 3 ?

Answer 1

Hint: It is given that a coin is tossed and die is rolled simultaneously. The number of possible outcomes in tossing a coin is 2 and the number of possible outcomes of rolling a die is 6. Therefore the number of possible outcomes when both occur simultaneously is \[2 \times 6\]. The sample space of an experiment or random trial is the set of all possible outcomes or results of that experiment.

Complete step by step solution:
The given events are throwing of a dice and tossing of a coin. Let, “H” is the event where the coin shows head and “T” is the event where the coin shows tail. Now, the sample space for the given events can be written as,the probability of the given event can be obtained using the formula, number of favorable outcomes divided by the total number of outcomes.
\[P\left( {head} \right) = \dfrac{1}{2} \\
\Rightarrow P\left( 3 \right) = \dfrac{1}{6} \\
\therefore \dfrac{1}{2} \times \dfrac{1}{6} = \dfrac{1}{{12}} \\ \]
Hence, the probability that the coin shows heads and the die shows 3 is \[\dfrac{1}{{12}}\].

Note: Here, we are asked to find the probability of getting head on coin and number 6 on die. So firstly we should write down all the possible outcomes in the sample space. Then count the numbers in the sample space. Hence find the probability of the given event using the formula number of favorable outcomes divided by the total number of outcomes.