The probability that Eli chooses
winners in a row is
.
Further explanation:
Given:
Eli flips a fair coin to decide which team chooses as a winner.
Concept used:
The probability
of any event
can be calculated as follows:
…… (1)
Here,
is the total number of elements in event
and
is the number of element in sample space of an experiment.
Calculation:
The sample space is the total possible outcomes in an experiment.
Consider
as the number of element in sample space
.
The possible outcomes in sample space
are win and lose.
The sample space
is as follows:
![\boxed{S=\{H,T\}}](https://tex.z-dn.net/?f=%5Cboxed%7BS%3D%5C%7BH%2CT%5C%7D%7D)
Therefore, the number of element in sample space
is as follows:
Consider
as the event that Eli choosing the winner team,
as the number of favorable outcomes in event
and
as the probability of event
.
The winner is chooses if Eli flips the coin. There is chance that Eli chooses winner either head comes or tail comes.
Therefore, there is only one favorable outcomes to choose the winning team.
The number of favorable outcomes in an event
can be calculated as follows:
Substitute
for
and
for
in the equation (1) to obtain the probability
.
The probability that Eli chooses
winner in a row can be calculated as follows:
![\begin{aligned}P(A)&=\left(\dfrac{1}{2}\cdot \dfrac{1}{2}\cdot \dfrac{1}{2}\cdot \dfrac{1}{2}\cdot \dfrac{1}{2}\cdot \dfrac{1}{2}\cdot \dfrac{1}{2}\right)\\&=\dfrac{1}{2^{7}}\\&=\dfrac{1}{128}\\&=0.0078\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7DP%28A%29%26%3D%5Cleft%28%5Cdfrac%7B1%7D%7B2%7D%5Ccdot%20%5Cdfrac%7B1%7D%7B2%7D%5Ccdot%20%5Cdfrac%7B1%7D%7B2%7D%5Ccdot%20%5Cdfrac%7B1%7D%7B2%7D%5Ccdot%20%5Cdfrac%7B1%7D%7B2%7D%5Ccdot%20%5Cdfrac%7B1%7D%7B2%7D%5Ccdot%20%5Cdfrac%7B1%7D%7B2%7D%5Cright%29%5C%5C%26%3D%5Cdfrac%7B1%7D%7B2%5E%7B7%7D%7D%5C%5C%26%3D%5Cdfrac%7B1%7D%7B128%7D%5C%5C%26%3D0.0078%5Cend%7Baligned%7D)
Thus, the probability that Eli chooses
winner in a row is
.
Learn more:
1. Learn more about problem on circle brainly.com/question/9510228
2. Learn more about problem on graph brainly.com/question/2334270
Answer details:
Grade: Senior school
Subject: Mathematics
Chapter: Probability
Keywords: Probability, Eli, favorable outcomes, event, experiment, winner, sample space, fair coin, number of element, 7 winners, in a row, basic probability theorem.