00:01
In this problem, it is said that you randomly guess the answers to the first four questions on a test.
00:06
Each question has four choices and one correct answer, and we need to find the probability that you choose the correct answer for all four questions.
00:15
So what are we going to do? here we are going to consider c to be the event that you choose the correct answer for a question.
00:22
Then what will the probability of this event c be? well, this will be the number of favorable outcomes divided by the total number of outcomes.
00:29
Now, there is only one correct answer, and so one favorable outcome, and there are four choices, so there are four outcomes in total.
00:37
So pfc is 1 over 4.
00:39
Now, we want to find the probability that you choose the correct answer for all four questions.
00:43
So we want to find the probability that you select the correct answer for the first question, and you select the correct answer for the second question, and you select the correct answer for the third one, and also for the fourth one.
00:54
Now, note that these four events are independent events...