Suppose that 1800 people are all playing a game for which the chance of winning is $49 \%$. 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?
$P($ five wins in a row) $=\square$
(Round to three decimal places as needed.)
Answer
So, the probability of one person winning five games in a row is \(\boxed{0.028}\).
Step 1 ：Suppose that 1800 people are all playing a game for which the chance of winning is 49%. Assuming everyone plays exactly five games, we want to find the probability of one person winning five games in a row.
Step 2 ：The probability of winning one game is 49%, or 0.49. Since the games are independent, the probability of winning five games in a row is simply \(0.49^5\).
Step 3 ：Calculating this gives a probability of approximately 0.028.
Step 4 ：So, the probability of one person winning five games in a row is \(\boxed{0.028}\).
