Questions: Suppose that 1800 people are all playing a game for which the chance of winning is 47%. Complete parts (a) and (b) below. a. Assuming everyone plays exactly four games, what is the probability of one person winning four games in a row? P (four wins in a row) = 0.049 (Round to three decimal places as needed.) On average, how many of the 1800 people could be expected to have a "hot streak" of four games? (Round to the nearest whole number as needed.)

Suppose that 1800 people are all playing a game for which the chance of winning is 47%. Complete parts (a) and (b) below.
a. Assuming everyone plays exactly four games, what is the probability of one person winning four games in a row?
P (four wins in a row) = 0.049
(Round to three decimal places as needed.)
On average, how many of the 1800 people could be expected to have a "hot streak" of four games?
(Round to the nearest whole number as needed.)

Transcript text: Suppose that 1800 people are all playing a game for which the chance of winning is $47 \%$. Complete parts (a) and (b) below. a. Assuming everyone plays exactly four games, what is the probability of one person winning four games in a row? $P$ (four wins in a row) $=0.049$ (Round to three decimal places as needed.) On average, how many of the 1800 people could be expected to have a "hot streak" of four games? (Round to the nearest whole number as needed.)

Solution

Solution Steps

Step 1: Finding the probability of winning four games in a row

Given that the probability of winning one game is 47% or 0.47, the probability of winning four games in a row is 0.47 * 0.47 * 0.47 * 0.47 = 0.049. This value is already provided in the problem.

Step 2: Calculate the expected number of people with a "hot streak"

Out of 1800 people, the number of people expected to have a "hot streak" of four wins is calculated by multiplying the total number of people by the probability of winning four games in a row. Thus, 1800 * 0.049 ≈ 88.2.

Step 3: Rounding to the nearest whole number

Since we're dealing with people, we must round to the nearest whole number. In this case, 88.2 rounds to 88.