Answer:
a) There are 1024 ways to answer the 5 questions
b)The probability is 0.000976
c) The probability is 0.014648
d) The probability is 0.015624
Explanation:
The number of ways to answer the 5 questions can be calculate as a rule of multiplication in which we have 4 answers for every questions, as:
4 * 4 * 4 * 4 * 4 = 1024
1st question 2nd 3rd 4th 5th
Then there are There are 1024 ways to answer the 5 questions.
On the other hand, the probability of get one question right is
or 0.25. Because there is only one answer correct from 4 possibles answers.
At the same way the probability of gt one question wrong is 3/4 or 0.75. Because there are 3 answers incorrect from 4 possible choices.
So, the probability of get 5 questions right, is the multiplication of probabilities of get the right answer in every question:
P= 0.25*0.25*0.25*0.25*0.25=0.000976
For calculate the probability of getting exactly 4 questions right and 1 wrong, we have five events with their respective probabilities:
1. The wrong answer is the first one:
P=0.75*0.25*0.25*0.25*0.25=0.002929
2. The wrong answer is the second one:
P=0.25*0.75*0.25*0.25*0.25=0.002929
3. The wrong answer is the third one:
P=0.25*0.25*0.75*0.25*0.25=0.002929
4. The wrong answer is the fourth one:
P=0.25*0.25*0.25*0.75*0.25=0.002929
5. The wrong answer is the fifth one:
P=0.25*0.25*0.25*0.75*0.25=0.002929
So the probability of getting exactly 4 questions right and 1 wrong is the sum of probabilities of all the event mentioned:
P=0.002929+0.002929+0.002929+0.002929+0.002929
P=0.014648
Finally the probability of doing well is the probability of having exactly 4 questions right and 1 wrong plus the probability of getting all 5 questions right:
P=0.014648+0.000976
P=0.015624