# Three students

Three students independently try to solve the problem. The first student will solve a similar problem with a probability of 0.6, the second student will solve at a probability of 0.55, and the third will solve at a probability 0.04. The problem is resolved, What is the probability that the first student has solved it?

Correct result:

p =  0.496

#### Solution:

$p_{1}=0.6 + 0.55 - 0.6 \cdot \ 0.55=0.82 \ \\ p_{2}=p_{1} + 0.04 - p_{1} \cdot \ 0.04=0.82 + 0.04 - 0.82 \cdot \ 0.04=\dfrac{ 517 }{ 625 }=0.8272 \ \\ \ \\ p=0.6 \cdot \ p_{2}=0.6 \cdot \ 0.8272=0.496$

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