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

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for