A.John is considering the investment opportunities of a stock. After detail analysis, He concluded that there are only five possible return in the coming year. The probability of getting these five possible returns are stated in the following table.
Return (%) -9 -5 3 4 10
Probability 0.05 0.2 0.1 X 0.25
(i) What is the value of “X” in the table above?
(ii) What is the expected return of this stock?
E(expected value)=-9x0.05+-5x0.2+3x0.1+4xX+10x0.25
B.Three students X, Y and Z, each shoot at a target. The probability of hitting the target by X, Y and Z are 1/3, 5/7 and 2/5 respectively.
(answers to 4 decimal places)
(i) Find the probability that all miss the target.
(ii) Find the probability that only two students hits the target.
(iii) Find the probability that at least one student could hit the target.
(iv) If these three students shoot at a target sequentially, what is the probability that only Y could hit the target?
(Hint: X shoot first, then Y shoot and finally Z will shoot.)