Using the binomial distribution formula, the probability of a particular student being promoted to the next semester is approximately 0.9998 or 99.98%.
The number of subjects that the course has = 10
The number of courses the student needs to clear for promotion, x ≥ 4
The probability of a student passing any subject = 75%
P(X ≥ 4)
Using the binomial distribution formula:
P(X ≥ 4) = 1 - P(X < 4)
= 1 - [P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)]
= 1 - [(10 choose 0) * 0.75^0 * 0.25^10 + (10 choose 1) * 0.75^1 * 0.25^9 + (10 choose 2) * 0.75^2 * 0.25^8 + (10 choose 3) * 0.75^3 * 0.25^7]
= 1 - [0.000000056 + 0.000000953 + 0.000013962 + 0.000197887]
= 1 - 0.000212858 = 0.999787142
Thus, the probability of a particular student being promoted to the next semester is approximately 0.9998 or 99.98%.
Complete Question:
A course has 10 subjects, and the student has to clear at least 4 courses to be promoted to the next semester. The probability of passing any course is 75%. What is the probability of a particular student being promoted to the next semester?