Alright, let's solve this step-by-step.
1. Understanding the Probability:
- The probability of a red flower in the offspring is given as [tex]\( \frac{1}{6} \)[/tex].
- From this, we know that the probability of a white flower in the offspring is [tex]\( 1 - \frac{1}{6} = \frac{5}{6} \)[/tex].
2. Total Number of Offspring:
- We are given that there are 777 offspring in total.
3. Calculating the Expected Number of Red-Flowered Plants:
- The expected number of red-flowered plants can be found by multiplying the total number of offspring by the probability of having red flowers.
- This is [tex]\( 777 \times \frac{1}{6} \)[/tex].
4. Calculating the Expected Number of White-Flowered Plants:
- Since the total number of offspring is 777, the number of white-flowered plants will be the total number of offspring minus the number of red-flowered plants.
- This is [tex]\( 777 - (777 \times \frac{1}{6}) \)[/tex].
Using these steps, we find that:
- The expected number of red-flowered plants is approximately 129.5.
- Subtracting this from the total, the expected number of white-flowered plants will be 647.5.
Therefore, in a population of 777 offspring from such a cross, we would expect approximately 647.5 white-flowered plants.
