Question

Cross-fertilizing a red and a white flower produces red flowers 25% of the time. now we cross-fertilize five pairs of red and white flowers and produce five offspring. find the probability that there will be no red-flowered plants in the five offspring.

Answer 1

In a cross-fertilization between red and white flowers, the probability of having no red-flowered plants in five offspring can be calculated using the binomial probability formula. The probability is approximately 23.73%.

Step-by-step explanation:

In a cross-fertilization between a red and a white flower, where red flowers are produced 25% of the time, the probability of having no red-flowered plants in five offspring can be calculated using the binomial probability formula. The formula is:

P(X=k) = (n C k) * p^k * (1-p)^(n-k)

where:

• P(X=k) is the probability of getting exactly k successes (in this case, zero red-flowered plants)
• n is the total number of trials (in this case, five offspring)
• k is the number of successful outcomes (in this case, zero red-flowered plants)
• p is the probability of success (in this case, 25% or 0.25)

Using the formula with the given values, we get:

P(X=0) = (5 C 0) * 0.25^0 * (1-0.25)^(5-0)

P(X=0) = 1 * 1 * 0.75^5

P(X=0) = 0.75^5

P(X=0) = 0.2373

Therefore, the probability that there will be no red-flowered plants in the five offspring is approximately 0.2373 or 23.73%.