Question

Gregor likes breeding different flowers in his garden. He noticed that when he breeds a white flower with a purple flower, most of the offspring are purple. To check that, he bred them again and obtained \[10\] offspring, and all of them were purple. Let's test the hypothesis that the offspring have equal chances of \[50\%\] of being either white or purple versus the alternative that the chance of a purple offspring is greater. Assuming the hypothesis is correct, what is the probability of getting \[10\] purple offspring out of \[10\]? Round your answer, if necessary, to the nearest tenth of a percent. \[\quad\] Let's agree that if the observed outcome has a probability less than \[1\%\] under the tested hypothesis, we will reject the hypothesis. What should we conclude regarding the hypothesis?

Answer 1

The probability of obtaining 10 purple offspring out of 10, assuming equal chances of 50% for white and purple, is approximately 0.1%.

Since this probability is less than 1%, we can reject the hypothesis and conclude that the chance of a purple offspring is greater than 50%.

Step-by-step explanation:

The probability of obtaining 10 purple offspring out of 10, assuming the hypothesis that the offspring have a 50% chance of being either white or purple, can be calculated using the binomial probability formula.

The formula is: P(X=k) = C(n,k) * p^k * (1-p)^(n-k).

{ Where P(X=k) is the probability of getting k purple offspring out of n, C(n,k) is the number of combinations of n items taken k at a time (use the formula C(n,k) = n! / (k!(n-k)!)), p is the probability of getting a purple offspring (0.5 in this case), and (1-p) is the probability of getting a white offspring (0.5 in this case).}

The probability of getting 10 purple offspring out of 10 can be calculated as follows:

C(10,10) * 0.5^10 * (1-0.5)^(10-10) = 1 * 0.5^10 * 0.5^0

= 0.5^10

= 0.0009765625

Convert the result to a percentage: 0.0009765625 * 100

= 0.09765625%

Therefore, the probability of obtaining 10 purple offspring out of 10, assuming the hypothesis that the offspring have a 50% chance of being either white or purple, is approximately 0.1%.

Since this observed outcome has a probability less than 1%, we can reject the hypothesis and conclude that the chance of a purple offspring is greater than 50%.