How to solve the following problems?
1. X throws a coin for 3 times. If he gets a head all the 3 times he is to get a price of $200. The entry fee for the game is $24. Find the expectation of X. (ans. $4)
2. X and Y with equal skill leave a game when X scores 12 points and Y 13 points. If the game was to finish at 15, what is their respective probability of winning? (ans. 5/16, 11/16)
3. X, one of the 5 horses entered into a race and is to be ridden by one of the 2 jockeys A and B. It is 3:1 that A rides X, in which case all the horses are equally likely to win. If B rides X, his chance is doubled. What are the odds in favour of its winning? (ans. 1:3)
4. X has 4 shares in a lottery in which there are 4 prizes, and 5 blanks. Y has 3 shares in another lottery in which there are 3 prizes and 4 blanks. Who has the better chance of winning exactly one prize? And who of winning 2 prizes?
5. If on an average 1 out of 10 vessels is worked, find the probability that out of 5 vessels expected to arrive, 4 at least will arrive safely? (ans. 0.92)
You have posted 5 problems with no indication of your own work so there is no way to determine what kinds of hints would help you. Are you taking a class in Probabiity? Do you know what "expectation" means? Do you know the probabiity that three coins in succession will all come up heads? These seem to be exercises in "binomia probability". What do you know about that?
1. I thought of solving this problem like this-
E(X)= X*p= (200-24)* (1/2)^3= 22 But the answer is 4.
2. I've no idea how to solve this one.
3. No idea!
4. No idea!
5. I thought of solving this problem like this-
P(A)= 1/10 and P(B)=9/10
Required probability= P(AAAAA)+P(AAAAB)*4= (1/10)^5 + (1/10)^4*(9/10)*5= 46/100000 But the answer is 0.92.