Assume that about 56% of population belong to group type of O.
A) What is the probability that it will need to take a blood test from exactly three individuals in order to find a person with O-type blood?
B) What is the probability that it will need to take more than 4 blood tests?
My attempt of A):
n = 3
k = ?
n-k = 3-?
p = 56% = 14/25
q = 1-p = 11/25
C(n,k)p^k * q^(n-k)
I am not sure how to use given information to solve this problem. Can you give me any hint please?
2026-03-26 07:57:30.1774511850
Probability involing percentages (Bernoulli?)
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We want the probability that we try once, fail, try again, fail, try again, got it. So the probability is $(0.44)(0.44)(0.56)$. .
For B), we want the probability that we fail $4$ times in a row. For that's exactly the situation in which we need more than $4$ trials.
Remark: It is best to get a handle on the problem, then use (if necessary) the appropriate formula.