Math  /  Data & Statistics

QuestionSuppose that 1700 people are all playing a game for which the chance of winning is 46%46 \%. Complete parts (a) and (b) below. a. Assuming everyone plays exactly five games, what is the probability of one person winning five games in a row? P(\mathrm{P}( five wins in a row )=)= \square (Round to three decimal places as needed.)

Studdy Solution

STEP 1

1. The probability of winning a single game is 0.46 0.46 .
2. Each game is independent of the others.
3. The probability of winning five games in a row is the product of the probabilities of winning each game.

STEP 2

1. Identify the probability of winning a single game.
2. Calculate the probability of winning five games in a row.
3. Round the result to three decimal places.

STEP 3

The probability of winning a single game is given as:
P(win one game)=0.46 P(\text{win one game}) = 0.46

STEP 4

To find the probability of winning five games in a row, multiply the probability of winning a single game by itself five times:
P(five wins in a row)=(0.46)5 P(\text{five wins in a row}) = (0.46)^5

STEP 5

Calculate (0.46)5 (0.46)^5 :
(0.46)5=0.046656 (0.46)^5 = 0.046656

STEP 6

Round the result to three decimal places:
P(five wins in a row)0.047 P(\text{five wins in a row}) \approx 0.047
The probability of one person winning five games in a row is:
0.047 \boxed{0.047}

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