what is the probability of getting all questions right on a 15 question, 3 multiple choice (each) with just guessing?
i did 15 C 3 and got 1/455
or is it (1/3)^15??
prob(right) = 1/3
prob(all 15 correct)
= C(15,15) (1/3)^15 (2/3)^0
= 1/3)^15
To calculate the probability of getting all questions right on a 15-question multiple-choice test with 3 choices per question by just guessing, you need to consider the probability of guessing the correct answer on each question.
Since there are 3 choices per question and you are guessing, the probability of guessing the correct answer on a single question is 1/3.
Now, to find the probability of guessing all 15 questions correctly, you need to multiply the individual probabilities together since the events are independent. In other words, the probability of both event A (guessing the first question correctly) and event B (guessing the second question correctly) happening is equal to the probability of event A multiplied by the probability of event B.
Using the multiplication rule, you can calculate the probability as follows:
P(guessing all 15 questions correctly) = (1/3) * (1/3) * (1/3) * ... * (1/3) [15 times]
Since there are 15 questions, you need to multiply the probability (1/3) by itself 15 times.
Therefore, the probability of getting all 15 questions right by just guessing is:
(1/3) * (1/3) * (1/3) * ... * (1/3) [15 times] = (1/3)^15 = 1/14,348,907.
Hence, the correct probability is 1/14,348,907, which is approximately 0.00000696 or 0.0007%.