two teams play a series of games, wher both teams have an equal probability of winning each game. its a best- of-five series, so the frist team to win three games is the winner. what is the probability that the series lasts five games

0.375

Step-by-step explanation:

With equal probability, hence

p for both teams = 0.5

First team to win three games win, probability that series lasts 5 games :

This means after 4 games each of the teams must have won 2 each ; and the series decider will be on the 5th game :

Each team winning two games and any of the teams could be the eventual winner :

From binomial relation :

P(x = x) = nCx * p^x * q^(n-x)

q = 1 - p = 0.5

Team A :

Winning any 2 from 4 and winning the 5th

(4C2 * 0.5^2 * 0.5^2) * 0.5

0.375 * 0.5 = 0.1875

Team B :

(4C2 * 0.5^2 * 0.5^2) * 0.5

0.375 * 0.5 = 0.1875

Hence, the probability that series lasts five games is :

[4C2*0.5^2*0.5^2)*0.5]+[4C2*0.5^2*0.5^2)*0.5]

0.1875 + 0.1875

= 0.375

answer: .64

step-by-step explanation

set up the formula for standard deviation for this set of numbers, then simplify

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.