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.Dereck of the YouTube channel Veritasium offered to play the following Game with people on the streets of Australia (since that's where he lived at the time). Dereck would flip a coin. You would call the result either Heads or Tails. If you called it correct Dereck would give you 20 AUS dollars. If you called it wrong you owed Dereck 10 AUS Dollars (see this video to see how people reacted to the offer). Since you call it in the air we make the (simplifying) assumption the coin is Fair.

.Dereck of the YouTube channel Veritasium offered to play the following Game with people on the streets of Australia (since that's where he lived at the time). Dereck would flip a coin. You would call the result either Heads or Tails. If you called it correct Dereck would give you 20 AUS dollars. If you called it wrong you owed Dereck 10 AUS Dollars (see this video to see how people reacted to the offer). Since you call it in the air we make the (simplifying) assumption the coin is Fair.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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### Task Description Dereck of the YouTube channel Veritasium proposed a game to people on the streets of Australia. In this game, Dereck would flip a coin, and the participant would call the result either heads or tails. If the participant's call was correct, Dereck would give them 20 AUD. If the call was incorrect, the participant would owe Dereck 10 AUD. The coin is assumed to be fair since it is called in the air. **Questions:** **A.** What is the expected outcome of playing the game? **B.** What is the expected outcome for playing this game 10 times? **C.** Assuming each flip can be considered fair, model the number of wins and losses using a binomial distribution. Create a probability density function for the number of wins and losses you will have with 10 flips. **Additional Information:** - The task includes a video link illustrating how people reacted to the offer. - It encourages exploration of concepts like expected value and binomial distribution through a practical example.
Transcribed Image Text:### Task Description Dereck of the YouTube channel Veritasium proposed a game to people on the streets of Australia. In this game, Dereck would flip a coin, and the participant would call the result either heads or tails. If the participant's call was correct, Dereck would give them 20 AUD. If the call was incorrect, the participant would owe Dereck 10 AUD. The coin is assumed to be fair since it is called in the air. **Questions:** **A.** What is the expected outcome of playing the game? **B.** What is the expected outcome for playing this game 10 times? **C.** Assuming each flip can be considered fair, model the number of wins and losses using a binomial distribution. Create a probability density function for the number of wins and losses you will have with 10 flips. **Additional Information:** - The task includes a video link illustrating how people reacted to the offer. - It encourages exploration of concepts like expected value and binomial distribution through a practical example.
Expert Solution
Step 1

From the given information,

Dereck would flip a coin.

Result of the flip either Heads or Tails.

Here, the coin is fair. Hence, P(head)=1/2 and P(Tail)=1/2

If you called it correct Dereck would give you 20 AUS dollars.

If you called it wrong you owed Dereck 10 AUS Dollars.

A.

The probability distribution for the above game is,

X 20 -10
P(X) 1/2 1/2

 

Expected outcome of the game:

X 20 -10  
P(X) 1/2 1/2  
X*P(X) 10 -5 ∑XPX=5

 

E(X)=∑XPX=$5

Thus, the expected outcome for playing the game is $5.

 

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