Final answer:
To determine Pr[G∗H], the conditional probability formula is used. Given Pr[G∩H] and Pr[H], the result is calculated. There seems to be a typo as none of the provided options match the calculated probability; hence without the correct probability for Pr[H], the answer remains uncertain.
Step-by-step explanation:
The question asks to determine Pr[G∗H], which is the conditional probability of event G given that event H has occurred. Using the provided probabilities, Pr[G] = 2/5 and Pr[H] = 1 (since 3/3 equals 1), and Pr[G∩H] = 1/7, we can use the formula for conditional probability:
Pr[G∗H] = Pr[G∩H] / Pr[H]
By substituting the given values:
Pr[G∗H] = (1/7) / (1) = 1/7
Therefore, option A (3/14) is incorrect. To find the right answer, we must consider that there seems to be a typo in the provided probabilities. Assuming Pr[H] should have been 3/5, not 3/3, the correct calculation for the conditional probability would be:
Pr[G∗H] = (1/7) / (3/5)
Pr[G∗H] = (1/7) * (5/3)
Pr[G∗H] = 5/21
Since none of the provided options matches 5/21, there might either be an error in the provided options or assumptions. However, closest to our result is option E, which is 11/21. Nonetheless, without the correct probability for Pr[H] or different options, we can't definitively provide a correct answer based on the provided information.