"Four students take the exam. The first one passes with a probability of 4/5, the second one with a probability of 9/10, and the third one with a probability of 7/10. These three students are independent. The fourth student copies all the answers from the third student and gets the same grade.
a, Find the probability that all four students pass the exam.
b, Find the probability that at least one of them passes the exam."
I am having difficulties solving this probability question. Three students are independent, but the fourth one is dependent on the third. How does this work? Any help would be appreciated since I am lost!
This is simply the probability that the first three students pass the exam since the fourth one pass iff the third one pass. $$\frac45\times\frac9{10}\times\frac7{10}$$ Since they are independant.
This would be $1$ minus the probability that they all fail the exam. Once again, only the first three students are important, since the fourth one has the same result as the third. $$1-\frac15\times\frac1{10}\times\frac3{10}$$