Answer to Question #277037 in Statistics and Probability for THEASAMOAH

Question

Amir and Jingpeng each play a single round of a computer game, which ends with a win or a loss. Let A denote the event that Amir loses, and J denote the event that Jingpeng loses the game they play, respectively. Suppose that P(A) = 1/9 and P(J) = 1/12. We assume that the events A and J are independent.

Find the probability that:

(i) Jingpeng wins the game it plays.

(ii) Both of them lose the game they play.

(iii) At least one of them loses the game they play.

(iv) Both of them win the game they play.

Answer 1

Let A denote the event that Amir loses, and J denote the event that Jingpeng loses the game they play, respectively.

P(A) = 1/9

P(J) = 1/12

(1). 1-P(J)

$= 1-\frac{1}{12}$

$= \frac{11}{12}$

(2). P(A)n(J) = P(A)*P(J)

=$\frac{1}{9} *\frac{1}{12}$

=$\frac{1}{108}$

(3). probability at least one loses the game

= P(A)nP(J') or P(J)nP(A')

= $\frac{1}{9}* \frac {11}{12}+\frac{8}{9}*\frac{1}{12}$

= $\frac{89}{108}$

(4).P(A uJ) =P(A)*P(J) - P(AnJ)

=$\frac{1}{9}+ \frac{1}{12} - \frac{1}{108}$

=$\frac{1}{54}$