SOLUTION: A student sits a true/false test with 10 questions and he guesses everyone. How do you describe the probability distribution for the number of correct guesses and also present the

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Question 1137297: A student sits a true/false test with 10 questions and he guesses everyone. How do you describe the probability distribution for the number of correct guesses and also present the probability distribution in a table
Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
There are 11 possible total correct answers, 0-10. Since each answer has exactly a 50/50 chance of being correct, the midpoint, '5', will have the highest probability of being the total number of correct answers. The probability graph (or table) will be a bell curve. The probability of '5' is the highest, '4' and '6' are the next highest, then '3' and '7', etc., all the way down to '0' and '10'.

P(10 correct) = 0.5%5E10 = 0.00098
P(9 correct) = %280.5%29%5E9+%2A+%280.5%29%5E1+%2A+%2810%21%2F%289%21%2A1%21%29%29 = 0.00977
P(8 correct) = %280.5%29%5E8+%2A+%280.5%29%5E2+%2A+%2810%21%2F%288%21%2A2%21%29%29 = 0.04395
P(7 correct) = %280.5%29%5E7+%2A+%280.5%29%5E3+%2A+%2810%21%2F%287%21%2A3%21%29%29 = 0.11719
P(6 correct) = %280.5%29%5E6+%2A+%280.5%29%5E4+%2A+%2810%21%2F%286%21%2A4%21%29%29 = 0.20508
P(5 correct) = %280.5%29%5E5+%2A+%280.5%29%5E5+%2A+%2810%21%2F%285%21%2A5%21%29%29 = 0.24609
P(4 correct) = %280.5%29%5E4+%2A+%280.5%29%5E6+%2A+%2810%21%2F%284%21%2A6%21%29%29 = 0.20508
P(3 correct) = %280.5%29%5E3+%2A+%280.5%29%5E7+%2A+%2810%21%2F%283%21%2A7%21%29%29 = 0.11719
P(2 correct) = %280.5%29%5E2+%2A+%280.5%29%5E8+%2A+%2810%21%2F%282%21%2A8%21%29%29 = 0.04395
P(1 correct) = %280.5%29%5E1+%2A+%280.5%29%5E9+%2A+%2810%21%2F%281%21%2A9%21%29%29 = 0.00977
P(0 correct) = 0.5%5E10 = 0.00098