What is the probability

Question

It is known that 65% of high school students study for the exam. What is the probability that 3 students will not study for the exam?

Answer 1

Hi Kat,

The situation can be understood through binomial probability. We have three students and each student either studies or doesn't study for the exam. The probability that his student will study is 65% which means the probability that a student will not study is 35%. Define the probability that all three students will not study, we use the binomial probability formul the binomial probability formula, which is P (X = K) = (N choose K) * (p^k) * ((1-p)^(n-k)).

P(X = K) is the probability of exactly K successes in N trials

N choose K is the number of combinations of N items taken k at a time

p is the probability of success on a given trial

n is the number of trials

k is the number of successes

In this case:

n = 3 (number of students)

k = 3 (we want all three to not study)

p = 0.35 (probability that student will not study)

Plugging these into the formula, gives:

P(X = 3) = (3 choose 3) * (0.35^3) * ((1-0.35)^(3-3))

The calculated probability is approximately 4.29%.

I hope this helps! Please feel free to contact me with any further questions, or if you would like to delve into this core component of statistics more deeply together.

Thank you,

Benjamin M.