To find the probability that Joe picks two sweets of different flavors, we need to consider the total number of ways to pick two sweets and the number of favorable outcomes where the two sweets are of different flavors.

1. Calculate the total number of ways to pick two sweets from the bag:
- The bag contains 7 strawberry and 9 blueberry sweets, making a total of 16 sweets.
- The number of ways to pick 2 sweets out of 16 is given by the combination formula $ \binom{n}{k} $, which is $ \frac{n!}{k!(n-k)!} $.

$$
\binom{16}{2} = \frac{16!}{2!(16-2)!} = \frac{16 \times 15}{2 \times 1} = 120
$$

2. Calculate the number of favorable outcomes where the two sweets are of different flavors:
- Joe can pick one strawberry and one blueberry.
- The number of ways to pick 1 strawberry out of 7 is $ \binom{7}{1} = 7 $.
- The number of ways to pick 1 blueberry out of 9 is $ \binom{9}{1} = 9 $.
- The total number of favorable outcomes is $ 7 \times 9 = 63 $.

3. Calculate the probability:
- The probability is the number of favorable outcomes divided by the total number of outcomes.

$$
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{63}{120}
$$

4. Simplify the fraction:
- Find the greatest common divisor (GCD) of 63 and 120, which is 3.
- Divide both the numerator and the denominator by their GCD.

$$
\frac{63 \div 3}{120 \div 3} = \frac{21}{40}
$$

Therefore, the probability that Joe picks two sweets of different flavors is $ \frac{21}{40} $.

Question

To find the probability that Joe picks two sweets of different flavors, we need to consider the total number of ways to pick two sweets and the number of favorable outcomes where the two sweets are of different flavors.

1. Calculate the total number of ways to pick two sweets from the bag:
   - The bag contains 7 strawberry and 9 blueberry sweets, making a total of 16 sweets.
   - The number of ways to pick 2 sweets out of 16 is given by the combination formula $ \binom{n}{k} $, which is $ \frac{n!}{k!(n-k)!} $.

$$
   \binom{16}{2} = \frac{16!}{2!(16-2)!} = \frac{16 \times 15}{2 \times 1} = 120
   $$

2. Calculate the number of favorable outcomes where the two sweets are of different flavors:
   - Joe can pick one strawberry and one blueberry.
   - The number of ways to pick 1 strawberry out of 7 is $ \binom{7}{1} = 7 $.
   - The number of ways to pick 1 blueberry out of 9 is $ \binom{9}{1} = 9 $.
   - The total number of favorable outcomes is $ 7 \times 9 = 63 $.

3. Calculate the probability:
   - The probability is the number of favorable outcomes divided by the total number of outcomes.

$$
   \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{63}{120}
   $$

4. Simplify the fraction:
   - Find the greatest common divisor (GCD) of 63 and 120, which is 3.
   - Divide both the numerator and the denominator by their GCD.

$$
   \frac{63 \div 3}{120 \div 3} = \frac{21}{40}
   $$

Therefore, the probability that Joe picks two sweets of different flavors is $ \frac{21}{40} $.

Knowee AI · Accepted Answer

To find the probability that Joe picks two sweets of different flavors, we need to consider the total number of ways to pick two sweets and the number of favorable outcomes where the two sweets are of different flavors.

1. Calculate the total number of ways to pick two sweets from the bag:
   - The bag contains 7 strawberry and 9 blueberry sweets, making a total of 16 sweets.
   - The number of ways to pick 2 sweets out of 16 is given by the combination formula $ \binom{n}{k} $, which is $ \frac{n!}{k!(n-k)!} $.

$$
   \binom{16}{2} = \frac{16!}{2!(16-2)!} = \frac{16 \times 15}{2 \times 1} = 120
   $$

2. Calculate the number of favorable outcomes where the two sweets are of different flavors:
   - Joe can pick one strawberry and one blueberry.
   - The number of ways to pick 1 strawberry out of 7 is $ \binom{7}{1} = 7 $.
   - The number of ways to pick 1 blueberry out of 9 is $ \binom{9}{1} = 9 $.
   - The total number of favorable outcomes is $ 7 \times 9 = 63 $.

3. Calculate the probability:
   - The probability is the number of favorable outcomes divided by the total number of outcomes.

$$
   \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{63}{120}
   $$

4. Simplify the fraction:
   - Find the greatest common divisor (GCD) of 63 and 120, which is 3.
   - Divide both the numerator and the denominator by their GCD.

$$
   \frac{63 \div 3}{120 \div 3} = \frac{21}{40}
   $$

Therefore, the probability that Joe picks two sweets of different flavors is $ \frac{21}{40} $.

Q5) A bag of sweets contains 7 strawberry, 9 blueberry. Joe picks two sweets at random. Find the probability that Joe picks two sweets that are different flavours. Write your answer as a SIMPLIFIED fraction using the / symbol.

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