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3 years ago

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Suppose % of all . (a) What is the probability that two in a row? (b) What is the probability that in a row? (c) When even

ts are independent, their complements are independent as well. Use this result to determine the probability that in a row, but in a row. (a) The probability that two in a row is . 1156. (Round to four decimal places as needed.) (b) The probability that in a row is . 0393. (Round to four decimal places as needed.) (c) The probability that in a row, but in a row is

1 answer:

Pachacha [2.7K]3 years ago

5 0

Complete Question:

Suppose George wins 34% of all chess games. 

(a) What is the probability that George wins two chess games in a row?

(b) What is the probability that George wins three chess games in a row? 

(c) When events are independent, their complements are independent as well. Use this result to determine the probability that George wins three chess games in a row, but does not win four in a row.

Answer:

(a) $Probability = 0.1156$

(b) $Probability = 0.0393$

(c) $Probability = 0.0259$

Step-by-step explanation:

Represent Win with W

So, we have:

$W = 34\%$

Solving (a): Winning two in a row;

This is represented by WW and is calculated as thus:

$Probability = W * W$

$Probability = 34\% * 34\%$

$Probability = 0.1156$

Solving (b): Winning three in a row;

This is represented by WWW and is calculated as thus:

$Probability = W * W * W$

$Probability = 34\% * 34\% * 34\%$

$Probability = 0.039304$

$Probability = 0.0393$ (Approximated)

Solving (c): Wins three in a row but lost the fourth

Represent Losing with L

L is calculated as:

$L = 1 - W$ ---- Complement of probability

$L = 1 - 34\%$

$L = 66\%$

This probability is represented by WWWL and is calculated as thus:

$Probability = 34\% *34\% *34\% *66\%$

$Probability = 0.02594064$

$Probability = 0.0259$ (Approximated)

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If two events, A and B, are independent, we have that:

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This happens if A wins in 4 games of B wins in 4 games.

Probability of A winning in exactly four games:

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The probability that the series lasts exactly four games is $3p(1-p)(p^{2} + (1 - p)^{2})$

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