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Sure! Let's go through each part of the question step by step.
### 3.1 What is the probability that the card will be an odd number?
Step 1: Identify the total number of cards.
- The total number of cards is 6 (numbered 1, 2, 3, 4, 5, 6).
Step 2: Identify the odd numbers within this range.
- The odd numbers are 1, 3, and 5.
Step 3: Count the number of odd numbers.
- There are 3 odd numbers.
Step 4: Calculate the probability.
- The probability of drawing an odd number is the number of odd numbers divided by the total number of cards:
[tex]\[ \text{Probability of odd number} = \frac{\text{Number of odd numbers}}{\text{Total number of cards}} = \frac{3}{6} = \frac{1}{2} = 0.5 \][/tex]
### 3.2 What is the probability that it will be a prime number?
Step 1: Identify the total number of cards.
- The total number of cards is 6.
Step 2: Identify the prime numbers within this range.
- The prime numbers between 1 and 6 are 2, 3, and 5.
Step 3: Count the number of prime numbers.
- There are 3 prime numbers.
Step 4: Calculate the probability.
- The probability of drawing a prime number is the number of prime numbers divided by the total number of cards:
[tex]\[ \text{Probability of prime number} = \frac{\text{Number of prime numbers}}{\text{Total number of cards}} = \frac{3}{6} = \frac{1}{2} = 0.5 \][/tex]
### 3.3 What is the probability of drawing a card numbered 2?
Step 1: Identify the total number of cards.
- The total number of cards is 6.
Step 2: Identify the specific card number (2) and its occurrences.
- The number '2' appears once among these cards.
Step 3: Calculate the probability.
- The probability of drawing a card numbered 2 is the number of times 2 appears divided by the total number of cards:
[tex]\[ \text{Probability of drawing 2} = \frac{\text{Number of 2s}}{\text{Total number of cards}} = \frac{1}{6} \approx 0.1667 \][/tex]
### 3.4 What is the probability of drawing a card that is NOT numbered 1?
Step 1: Identify the total number of cards.
- The total number of cards is 6.
Step 2: Determine the cards that are not numbered 1.
- The numbers not equal to 1 are 2, 3, 4, 5, and 6.
Step 3: Count the number of cards that are not 1.
- There are 5 cards that are not numbered 1.
Step 4: Calculate the probability.
- The probability of drawing a card that is not numbered 1 is the number of non-1 cards divided by the total number of cards:
[tex]\[ \text{Probability of not drawing 1} = \frac{\text{Number of non-1 cards}}{\text{Total number of cards}} = \frac{5}{6} \approx 0.8333 \][/tex]
So, the probabilities for each question are:
- 3.1: 0.5
- 3.2: 0.5
- 3.3: 0.1667
- 3.4: 0.8333
### 3.1 What is the probability that the card will be an odd number?
Step 1: Identify the total number of cards.
- The total number of cards is 6 (numbered 1, 2, 3, 4, 5, 6).
Step 2: Identify the odd numbers within this range.
- The odd numbers are 1, 3, and 5.
Step 3: Count the number of odd numbers.
- There are 3 odd numbers.
Step 4: Calculate the probability.
- The probability of drawing an odd number is the number of odd numbers divided by the total number of cards:
[tex]\[ \text{Probability of odd number} = \frac{\text{Number of odd numbers}}{\text{Total number of cards}} = \frac{3}{6} = \frac{1}{2} = 0.5 \][/tex]
### 3.2 What is the probability that it will be a prime number?
Step 1: Identify the total number of cards.
- The total number of cards is 6.
Step 2: Identify the prime numbers within this range.
- The prime numbers between 1 and 6 are 2, 3, and 5.
Step 3: Count the number of prime numbers.
- There are 3 prime numbers.
Step 4: Calculate the probability.
- The probability of drawing a prime number is the number of prime numbers divided by the total number of cards:
[tex]\[ \text{Probability of prime number} = \frac{\text{Number of prime numbers}}{\text{Total number of cards}} = \frac{3}{6} = \frac{1}{2} = 0.5 \][/tex]
### 3.3 What is the probability of drawing a card numbered 2?
Step 1: Identify the total number of cards.
- The total number of cards is 6.
Step 2: Identify the specific card number (2) and its occurrences.
- The number '2' appears once among these cards.
Step 3: Calculate the probability.
- The probability of drawing a card numbered 2 is the number of times 2 appears divided by the total number of cards:
[tex]\[ \text{Probability of drawing 2} = \frac{\text{Number of 2s}}{\text{Total number of cards}} = \frac{1}{6} \approx 0.1667 \][/tex]
### 3.4 What is the probability of drawing a card that is NOT numbered 1?
Step 1: Identify the total number of cards.
- The total number of cards is 6.
Step 2: Determine the cards that are not numbered 1.
- The numbers not equal to 1 are 2, 3, 4, 5, and 6.
Step 3: Count the number of cards that are not 1.
- There are 5 cards that are not numbered 1.
Step 4: Calculate the probability.
- The probability of drawing a card that is not numbered 1 is the number of non-1 cards divided by the total number of cards:
[tex]\[ \text{Probability of not drawing 1} = \frac{\text{Number of non-1 cards}}{\text{Total number of cards}} = \frac{5}{6} \approx 0.8333 \][/tex]
So, the probabilities for each question are:
- 3.1: 0.5
- 3.2: 0.5
- 3.3: 0.1667
- 3.4: 0.8333
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