Three friends (A, B, and C) will participate in a round-robin tournament in which each one plays both of the others. Suppose that P(A beats B) = 0.5
P(A beats C) = 0.6
P(B beats C) = 0.9

and that the outcomes of the three matches are independent of one another.

a. What is the probability that A wins both her matches and that B beats C?
b. What is the probability that A wins both her matches?
c. What is the probability that A loses both her matches?
d. What is the probability that each person wins one match? (Hint: There are two different ways for this to happen.)

0.27 ; 0.30 ; 0.20 ; 0.21

Step-by-step explanation:

Given that :

P(A beats B) = 0.5

P(A beats C) = 0.6

P(B beats C) = 0.9

Since the outcomes are independent :

A.) probability that A wins both her matches and that B beats C

P(A beats B) * P(A beats C) * P(B beats C)

0.5 * 0.6 * 0.9 = 0.27

B.) probability that A wins both her matches

P(A beats B) * P(A beats C)

0.5 * 0.6 = 0.3

C.) probability that A loses both her matches?

(1 - P(A beats B)) * (1 - P(A beats C)

(1 - 0.5) * (1 - 0.6)

0.5 * 0.4 = 0.20

D.) probability that each person wins one match

Either (A beats B), (B beats C). (C beats A) OR (A beats C), (C beats B), (B beats A)

Hence;

(0.5 * 0.9 * (1 - 0.6)) + (0.6 * (1 - 0.9) * (1 - 0.5)) = 0.21

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1

answer: the center is the median and/or mean of the data. the spread is the range of the data. and, the shape describes the type of graph. the four ways to describe shape are whether it is symmetric, how many peaks it has, if it is skewed to the left or right, and whether it is uniform. good luck

step-by-step explanation: