Question

Let H = the proportion of Hal's crossword puzzles solved in under 30 minutes, and J = the proportion of Jose's crossword puzzles solved in under 30 minutes.

What is the probability that Jose's proportion of crossword puzzles solved in under 30 minutes is greater than Hal's?
A) 24%
B) 36%
C) 46%
D) 54%

Answer 1

The probability that Jose's proportion of crossword puzzles solved in under 30 minutes is greater than Hal's is 54%, thus the correct option is D.

Step-by-step explanation:

In order to calculate the probability that Jose's proportion of crossword puzzles solved in under 30 minutes is greater than Hal's, we need to compare the two proportions, H and J. To do this, we must first calculate the probability that Jose's proportion of puzzles solved in under 30 minutes is greater than or equal to Hal's. We can calculate this by subtracting H from 1, to get 1-H. This gives us the probability that Jose's proportion is greater than or equal to Hal's.

Now, to calculate the probability that Jose's proportion is strictly greater than Hal's, we must subtract the probability of Jose's proportion being equal to Hal's from the probability of Jose's proportion being greater than or equal to Hal's. We can calculate this probability by subtracting H squared from 1-H. This gives us the probability that Jose's proportion is strictly greater than Hal's, which is a 54%.