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?

Result

p =  0.496

Solution:

p1=0.6+0.550.6 0.55=0.82 p2=p1+0.04p1 0.04=0.82+0.040.82 0.04=517625=0.8272  p=0.6 p2=0.6 0.82720.4963=0.496p_{ 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 \doteq 0.4963 = 0.496



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