b) From a pack of flash cards numbered from 1 to 20, a card is drawn at random.
(i)
What is the probability of getting the card with odd number?
(ii) What is the probability of getting card with a number which is exactly
divisible by 3?
(iii) What is the probability of getting card with a number which is exactly
divisible by 5?
(iv) What is the probability of getting card with a number which is not exactly
divisible by 8?
a



Answer :

Certainly! Let's tackle each part of the question step-by-step.

We have a pack of flash cards numbered 1 to 20, and we're drawing one card at random.

### i) Probability of getting the card with odd number:

First, let's identify the odd numbers between 1 and 20. These numbers are:

[tex]\[ 1, 3, 5, 7, 9, 11, 13, 15, 17, 19 \][/tex]

There are 10 odd numbers. Therefore, the probability of drawing an odd-numbered card is:

[tex]\[ \text{Probability of odd number} = \frac{\text{Number of odd cards}}{\text{Total number of cards}} = \frac{10}{20} = 0.5 \][/tex]

### ii) Probability of getting card with a number which is exactly divisible by 3:

Now, let's identify the numbers between 1 and 20 that are divisible by 3. These numbers are:

[tex]\[ 3, 6, 9, 12, 15, 18 \][/tex]

There are 6 such numbers. Therefore, the probability of drawing a card with a number divisible by 3 is:

[tex]\[ \text{Probability of divisible by 3} = \frac{\text{Number of cards divisible by 3}}{\text{Total number of cards}} = \frac{6}{20} = 0.3 \][/tex]

### iii) Probability of getting card with a number which is exactly divisible by 5:

Next, let's identify the numbers between 1 and 20 that are divisible by 5. These numbers are:

[tex]\[ 5, 10, 15, 20 \][/tex]

There are 4 such numbers. Therefore, the probability of drawing a card with a number divisible by 5 is:

[tex]\[ \text{Probability of divisible by 5} = \frac{\text{Number of cards divisible by 5}}{\text{Total number of cards}} = \frac{4}{20} = 0.2 \][/tex]

### iv) Probability of getting card with a number which is not exactly divisible by 8:

Finally, let's identify the numbers between 1 and 20 that are not divisible by 8. The numbers that are divisible by 8 are:

[tex]\[ 8, 16 \][/tex]

There are 2 such numbers. Thus, the numbers that are not divisible by 8 are:

[tex]\[ 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20 \][/tex]

So, there are 18 such numbers. Therefore, the probability of drawing a card with a number not divisible by 8 is:

[tex]\[ \text{Probability of not divisible by 8} = \frac{\text{Number of cards not divisible by 8}}{\text{Total number of cards}} = \frac{18}{20} = 0.9 \][/tex]

### Summary:

The probabilities are as follows:
(i) Probability of getting the card with an odd number: [tex]\( 0.5 \)[/tex]
(ii) Probability of getting card with a number which is exactly divisible by 3: [tex]\( 0.3 \)[/tex]
(iii) Probability of getting card with a number which is exactly divisible by 5: [tex]\( 0.2 \)[/tex]
(iv) Probability of getting card with a number which is not exactly divisible by 8: [tex]\( 0.9 \)[/tex]