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Sample space of throwing a die and find the probability of:
1. Getting A no. Less than 4
2. Getting A composite no
3. Getting A nos. Which are multiple of 3
4. Getting even nos.
5. Getting odd nos.
6. Getting a no. Greater than six
7. Getting a number less than one
8. A prime no
Given:
A die is thrown.
To do:
We have to find the probability of
1. Getting A no. Less than 4
2. Getting A composite no
3. Getting A nos. Which are multiple of 3
4. Getting even nos.
5. Getting odd nos.
6. Getting a no. Greater than six
7. Getting a number less than one
8. A prime no
Solution:
When a die is thrown, the total possible outcomes are 1, 2, 3, 4, 5 and 6.
This implies,
The total number of possible outcomes $n=6$.
1. Numbers less than 4 are 1, 2, 3.
Total number of favourable outcomes $=3$.
We know that,
Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$
Therefore,
Probability of getting a number less than 4 $=\frac{3}{6}=\frac{1}{2}$
2. Composite numbers from 1 to 6 are 4 and 6
Total number of favourable outcomes $=2$.
We know that,
Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$
Therefore,
Probability of getting a composite number $=\frac{2}{6}=\frac{1}{3}$
3. Numbers which are multiples of 3 are 3, 6.
Total number of favourable outcomes $=2$.
We know that,
Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$
Therefore,
Probability of getting a multiple of 3 $=\frac{2}{6}=\frac{1}{3}$
4. Numbers which are even are 2, 4, 6.
Total number of favourable outcomes $=3$.
We know that,
Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$
Therefore,
Probability of getting an even number $=\frac{3}{6}=\frac{1}{2}$
5. Numbers which are odd are 1, 3, 5.
Total number of favourable outcomes $=3$.
We know that,
Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$
Therefore,
Probability of getting an odd number $=\frac{3}{6}=\frac{1}{2}$
6. There are no numbers greater than 6.
Total number of favourable outcomes $=0$.
We know that,
Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$
Therefore,
Probability of getting a number greater than 6 $=\frac{0}{6}=0$
7. There are no numbers less than 0 here.
Total number of favourable outcomes $=0$.
We know that,
Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$
Therefore,
Probability of getting a number less than 1$=\frac{0}{6}=0$
8. Numbers which are prime are 2, 3, 5.
Total number of favourable outcomes $=3$.
We know that,
Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$
Therefore,
Probability of getting a prime number $=\frac{3}{6}=\frac{1}{2}$.
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