Mathematics, 18.02.2020 04:26 cuki96

Two athletic teams play a series of games; the first team to win 4 games is declared the overall winner.
A) Suppose that one of the teams is stronger than the other and wins each game with probability .6 independently of the outcomes of the other games. Find that probability that the stronger team wins the series. (Hint: let X be the random variable that denotes the number of games necessary until the stronger team wins 4.)

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Answer from: 21shuldrak

Step-by-step explanation:

Considering for for stronger team, given that: P(winning) = 0.6This implies that Probability that the stronger team wins the first 4 games or Probability that the stronger team wins 3 games in the first 4 games and Probability that the stronger team wins the fifth game or Probability that the stronger team wins 3 of the first 5 games and Probability that the stronger team wins the 6th game or Probability that the stronger team wins 3 games in the first 6 games.This is the likely possibilities for the probability that the stronger team wins the series. Applying the concept of combinatorics and binomial probability(P(x) = r) ; nCr x P^r x q^n-rwhere q = probability of failure, probability of not winning = 1 - 0.4 = 0.6= 0.6^4 + 4C1 x 0.6^4 x 0.4 + 5C2 x 0.6^4 x 0.4^2 + 6C3 x 0.6^4 x 0.4^3 = 0.710208Therefore, probability that the stronger team wins the series = 0.710208

Answer from: Quest

$y> \frac{1}{3}x$ and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be = $\frac{1-0}{3-0} = \frac{1}{3}$ .

y-intercept of dotted line is y=0 only.

plugging slope m= $\frac{1}{3}$ and b=0 in slope-intercept form y=mx+b, we get

$y=\frac{1}{3}x$ .

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

$y> \frac{1}{3}x$ .

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be = $\frac{4-1}{0-3} = \frac{3}{-3}=-1$ .

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .
Write a system of inequalities to represent the shaded portion of the graph.

Answer from: Quest

step-by-step explanation:

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