Joseph sows 420 flower seeds.

For each flower seed the probability that it will produce a flower is 4/7
 
.

Work out an estimate for the number of these flower seeds that will produce a flower.



To find an estimate for the number of flower seeds that will produce a flower, we can use the concept of expected value in probability.

The expected number of flower seeds that will produce a flower can be calculated using the formula:

\[
\text{Expected number} = \text{Total number of seeds} \times \text{Probability of a seed producing a flower}
\]

Given:
- Total number of seeds = 420
- Probability of a seed producing a flower = \(\frac{4}{7}\)

So, the expected number of flower seeds that will produce a flower is:

\[
\text{Expected number} = 420 \times \frac{4}{7}
\]

Let's calculate this:

\[
\text{Expected number} = 420 \times \frac{4}{7} = 420 \times 0.5714 \approx 240
\]

Therefore, an estimate for the number of seeds that will produce a flower is **240**.

Would you like further details or have any questions? Here are 8 related questions:

1. What is the formula for expected value in probability?
2. How would the estimate change if the probability was different?
3. What is the significance of the fraction \(\frac{4}{7}\) in this problem?
4. How can we calculate the exact probability distribution for this scenario?
5. What assumptions are we making in this estimate?
6. How would this problem change if the number of seeds was different?
7. What is the expected number if the probability of producing a flower was 1 (certainty)?
8. Can you explain what the expected value means in real-world terms?

**Tip:** In probability, the expected value gives the long-term average outcome of a random event after many repetitions.

Learn how to estimate the number of flower seeds that will produce a flower using probability. This problem involves 420 seeds with a probability of 4/7 for each seed to produce a flower. Detailed calculation and explanation provided.

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