Question 1206492
No more than half of the students means 0, 1, or 2 students passed. This is a binomial distribution. The probability is
{{{0.15^5+5*0.85*0.15^4+10*0.85^2*0.15^3}}}.
The {{{0.15^5}}} term represents the probability that none of the students passed. Since each student as a 85% pass rate, they have a 15% fail rate.
The {{{5*0.85*0.15^4}}} term represents the probability that 1 student passed. The {{{0.85*0.15^4}}} is the probability that 1 student passes and 4 fail, and it is multiplied by {{{5}}} because there are 5 possible ways to pick a student that passes.
The final term {{{10*0.85^2*0.15^3}}} is for 2 students passing. Again, the {{{0.85^2*0.15^3}}} term is the probability that any 2 given students pass and the other 3 fail. There are {{{5C2=10}}} ways to pick these 2 students.
Plugging this into a calculator, we get the probability as 0.0266 (rounded to 4 decimal places).
If you need more precision, plug it into a calculator yourself either online or on an actual calculator.