Final answer:
To calculate the probability of no more than four of the 5 offspring being three-leafed soybeans, we need to consider the probabilities of each outcome and calculate the probabilities of the different combinations. Once we have the probabilities for each combination, we can add them up to find the final answer.
Step-by-step explanation:
To calculate the probability that among the 5 offspring no more than four of them are three-leafed soybeans, we need to consider the probability of each outcome. Firstly, we know that when a cross-fertilization of three-leafed and four-leafed soybeans occurs, the offspring are 40% four-leafed and the remaining offspring are three-leafed. So, the probability of an offspring being four-leafed is 40% or 0.4, and the probability of an offspring being three-leafed is 60% or 0.6.
To find the probability of no more than four of the 5 offspring being three-leafed, we need to consider the different possible combinations. These are: 0 four-leafed and 5 three-leafed, 1 four-leafed and 4 three-leafed, 2 four-leafed and 3 three-leafed, 3 four-leafed and 2 three-leafed, and 4 four-leafed and 1 three-leafed.
We can calculate the probability of each combination by multiplying the probabilities of the individual offspring. For example, the probability of having 1 four-leafed and 4 three-leafed offspring is 0.4 * 0.6 * 0.6 * 0.6 * 0.6 = 0.05184 or 5.184%. We can repeat this calculation for each combination and then add up the probabilities to get the final answer.