right now I'm trying to understand and solve this question for the practice purpose to learn the compounding probability and I'm kinda stuck to solve these 2 questions. Any advice and way to solve it is really welcome
- You would like to bet on who will win upcoming football match between 2 teams. You have 3 experts giving their prediction on who will win the match. Each expert has probability 0.6 that he will be right. You will decide who to bet on based on poll from the experts (you will bet on team whom 2 or 3 experts say will win). Under assumptions that the experts’ opinions are independent what is the probability that you will win your bet
- You would like to bet on who will win upcoming football match between 2 teams. You have 3 experts giving their prediction on who will win the match. Each expert has probability 0.6 that he will be right. You will decide who to bet on based on poll from the experts (you will bet on team whom 2 or 3 experts say will win). Under assumptions that the experts’ opinions are not independent what is the probability that you will win your bet
Edit: (For the first question) I have tried to separate the calculation to find the probability of 2 experts say win + (because the or statement) the probability of 3 experts say win but I'm stuck how to calculate the probability of 2 experts and 3 experts say win. Is that I need to use some sort of combination technique?
In the first case, the probability that all $3$ experts are right is $.6^3=.216$. The probability that exactly $2$ are right is $3\cdot.4\cdot.6^2=.432$, because there are $3$ ways to pick the expert who is wrong. The probability of success is $.216+.432=.648$
It's not possible to answer the second question without more information. For example, if all three experts always say the say thing, then the probability of success is $.6$, but if they don't always say the same thing, then it's something else, but we don't know what it is unless we know how the opinions depend on one another.