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(1) an even number and (2) a multiple of 3.

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Hint: This question is simply based on the definition of probability. Here we will first find the favourable events and then use a formula for finding the probability. In such a type of question where an occurrence of one event is a subset of the other event.

Complete step-by-step solution -

In the question it is given that an unbiased coin is thrown and we have to find the probability of getting an even number in the first part and a multiple of 3 in the second part.

Sample space when a dice is thrown is $\left\{ {1,2,3,4,5,6} \right\}$

$\therefore $ On throwing a dice total possible events =6

(1)

Here the favourable event is the occurrence of an even number.

Sample space of favourable event is $\left\{ {2,4,6} \right\}$

So total number of favourable events = 3.

Now, we know that the formula for finding probability is given as:

Probability = $\dfrac{{{\text{Total number of favourable events}}}}{{{\text{Total number of possible events}}}}$ .

Putting the values in above formula, we get:

Probability = $\dfrac{3}{6} = \dfrac{1}{2}$

(2)

Here the favourable event is the occurrence of a multiple of 3.

Sample space of favourable event is $\left\{ {3,6} \right\}$ .

So total number of favourable events = 2

Now, we know that the formula for finding probability is given as:

Probability = $\dfrac{{{\text{Total number of favourable events}}}}{{{\text{Total number of possible events}}}}$ .

Putting the values in above formula, we get:

Probability = $\dfrac{2}{6} = \dfrac{1}{3}$ .

Note: Before solving this type of question you should remember the formula for finding the probability. Here a dice is thrown. You should know that on throwing a dice the total number of possible events is equal to 6. And depending on what is given is a question you have to calculate the number of favourable events and then use the formula for finding the probability.

Complete step-by-step solution -

In the question it is given that an unbiased coin is thrown and we have to find the probability of getting an even number in the first part and a multiple of 3 in the second part.

Sample space when a dice is thrown is $\left\{ {1,2,3,4,5,6} \right\}$

$\therefore $ On throwing a dice total possible events =6

(1)

Here the favourable event is the occurrence of an even number.

Sample space of favourable event is $\left\{ {2,4,6} \right\}$

So total number of favourable events = 3.

Now, we know that the formula for finding probability is given as:

Probability = $\dfrac{{{\text{Total number of favourable events}}}}{{{\text{Total number of possible events}}}}$ .

Putting the values in above formula, we get:

Probability = $\dfrac{3}{6} = \dfrac{1}{2}$

(2)

Here the favourable event is the occurrence of a multiple of 3.

Sample space of favourable event is $\left\{ {3,6} \right\}$ .

So total number of favourable events = 2

Now, we know that the formula for finding probability is given as:

Probability = $\dfrac{{{\text{Total number of favourable events}}}}{{{\text{Total number of possible events}}}}$ .

Putting the values in above formula, we get:

Probability = $\dfrac{2}{6} = \dfrac{1}{3}$ .

Note: Before solving this type of question you should remember the formula for finding the probability. Here a dice is thrown. You should know that on throwing a dice the total number of possible events is equal to 6. And depending on what is given is a question you have to calculate the number of favourable events and then use the formula for finding the probability.