An unbiased dice is thrown. What is the probability of getting : 1)an even number or a multiple of 3 (2) an even number and a multiple of 3?

Question

Answer

There are six sample 1,2,3,4,5,6.
and even no 2,4,6 so, probability of even no is 3/6= (1/2)and in case of multiple of three,there are sample space 6 ,but sample3,6 ,so probability 2/6, so in case of 1 ,find union product, and 2 case find intersection ,you will find it,

Answer

Probability of getting a even number=
favorable cases / total cases = 3/6 = 2/3
probability of getting a multiple of 3=
3 and 6 are multiple of 3. so, favorable cases are only 2. And total cases are 6
probability is 2/6 = 1/3

Answer

1)   1/6 ( because only 6 is possible number in the dice which is a even number Or a multiple of 3.

Answer

Probability of getting an even number or a multiple of 3:

To find the probability of getting an even number or a multiple of 3 when throwing an unbiased dice, we need to determine the total number of favorable outcomes and the total number of possible outcomes.

Total number of favorable outcomes:
The favorable outcomes in this case are the numbers that satisfy either of the conditions: being even or being a multiple of 3.

Numbers that are even: 2, 4, and 6
Numbers that are multiples of 3: 3 and 6

So, the total number of favorable outcomes is 5.

Total number of possible outcomes:
An unbiased dice has six faces, numbered from 1 to 6. Therefore, the total number of possible outcomes is 6.

Probability:
The probability of an event is given by the ratio of favorable outcomes to the total number of possible outcomes.

Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

In this case, the probability of getting an even number or a multiple of 3 is:

Probability = 5 / 6

So, the probability is 5/6 or approximately 0.8333.

Probability of getting an even number and a multiple of 3:

To find the probability of getting an even number and a multiple of 3, we need to determine the total number of favorable outcomes and the total number of possible outcomes.

Total number of favorable outcomes:
The favorable outcomes in this case are the numbers that satisfy both conditions: being even and being a multiple of 3.

The only number that satisfies both conditions is 6.

So, the total number of favorable outcomes is 1.

Total number of possible outcomes:
An unbiased dice has six faces, numbered from 1 to 6. Therefore, the total number of possible outcomes is 6.

Probability:
The probability of an event is given by the ratio of favorable outcomes to the total number of possible outcomes.

Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

In this case, the probability of getting an even number and a multiple of 3 is:

Probability = 1 / 6

So, the probability is 1/6 or approximately 0.1667.

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