A true-false test consists of 15 items.
(a) If Chris does not study at all and guesses each and every item in the test, describe the probability model for the number of correct guesses.
each individual question has a probability of 1/2 of being correct
so you want (1/2)(1/2) .... (1/2) --- (15 times)
= (1/2)^15
= 3.051757813x-0.5
is that correct ?
that is the number for all correct (or incorrect)
see the answer to your other posted question
Yes, your calculation is correct. The probability model for the number of correct guesses in a true-false test for Chris, who does not study and guesses each item, can be determined by considering each individual question as an independent event with a probability of 1/2 of being correct.
To calculate the probability of getting all 15 items correct, you multiply the probability of getting one item correct (1/2) by itself 15 times:
(1/2) * (1/2) * (1/2) * ... * (1/2) (15 times)
= (1/2)^15
≈ 3.051757813x10^(-5) or 0.0000305176
So there is approximately a 0.003% chance that Chris will guess all 15 items correctly.