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 answer:

p =  0.4963

Step-by-step explanation:

$$\begin{gathered} p_1=0.6+0.55-0.6\cdot 0.55=0.82 \\ {p}_2=p_1+0.04-p_1\cdot 0.04=0.82+0.04-0.82\cdot 0.04={\displaystyle \frac{517}{625}}=0.8272 \\ p=0.6\cdot p_2=0.6\cdot 0.8272=0.4963 \end{gathered}$$

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