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Sagot :
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]
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]
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