Explanation
Solution
Given:
Total number of questions n=5
Number of possible answers for each question =4
Probability of getting a correct answer by guessing:
p=41=0.25
Probability of getting an incorrect answer:
q=1−p=1−0.25=0.75
We need to find the probability of at least one correct answer:
P(at least one correct)=1−P(no correct answers)
The probability of getting zero correct answers in 5 trials is:
P(X=0)=nC0⋅p0⋅qn
P(X=0)=5C0⋅(0.25)0⋅(0.75)5
P(X=0)=1⋅1⋅(0.75)5
P(X=0)=0.2373046875
Now, calculating the final probability:
P(X≥1)=1−0.2373046875
P(X≥1)=0.7626953125
Rounding to four decimal places:
P(X≥1)≈0.7627
Correct Option: 3
