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Rus_ich [418]
3 years ago
6

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
Mathematics
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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