Question

Alexandre has two brothers: Hugo and Romain. Every day Romain draws a

name out of a hat to randomly select one of the three brothers to wash the
dishes. Alexandre suspected that Romain is cheating, so he kept track of
the draws, and found that out of 12 draws, Romain didn't get picked even
once.
1
Let's test the hypothesis that each brother has an equal chance of
1/3
getting picked in each draw versus the alternative that Romain's
probability is lower.
Assuming the hypothesis is correct, what is the probability of Romain not
getting picked even once out of 12 times? Round your answer, if
necessary, to the nearest tenth of a percent.
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?
Choose 1 answer:
of
B
We cannot reject the hypothesis.
We should reject the hypothesis.

Answer 1

The probability of Romain not being picked in 12 draws under the assumption that he has an equal chance as his brothers is 0.71%. Since this probability is less than 1%, we should reject the hypothesis that Romain has an equal chance in each draw.

Step-by-step explanation:

The student is asking to calculate the probability of an event under a specific assumption and decide whether to reject the hypothesis based on the outcome of an experiment. In this case, Alexandre wants to test the hypothesis that every brother has an equal chance of 1/3 of getting picked to do the dishes.

The probability of Romain not being picked in a single draw is 2/3 because there are three brothers and the hypothesis suggests each has an equal chance of being selected. Since each draw is independent, the probability of Romain not being picked across 12 draws is (2/3)12. Calculating this, we get:

P(Romain not picked in 12 draws) = (2/3)12 = 0.0071 or 0.71%

Since this probability is less than 1%, according to the criteria given, we should reject the hypothesis that Romain has an equal chance of getting picked in each draw.