Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Experience the convenience of getting reliable answers to your questions from a vast network of knowledgeable experts. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
ANSWER
The expected value is $0
EXPLANATION
The wins or loses of this game are:
• $1 if HH
,• $5 if TT
,• -$3 if TH or HT
H is for heads and T is for tails.
First we have to see the probabilities of these events happen:
[tex]P(HH)=P(TT)=\frac{1}{4}[/tex]This is because the posible outcomes are 4: HH, TT, HT, TH. And in only one of these the coins are both heads or both tails.
The probability that they are different is:
[tex]P(HT\text{ or }TH)=\frac{1}{4}+\frac{1}{4}=\frac{2}{4}=\frac{1}{2}[/tex]The expected value is:
[tex]E=1\cdot P(HH)+5\cdot P(TT)-3\cdot P(HT\text{ or }TH)[/tex][tex]E=1\cdot\frac{1}{4}+5\cdot\frac{1}{4}-3\cdot\frac{1}{2}=\frac{1}{4}+\frac{5}{4}-\frac{3}{2}=\frac{1+5-6}{4}=\frac{6-6}{4}=0[/tex]The expected value is 0.
It is a fair game, because the expected value of the game is 0. This means that the cost of playing (which would be the cost of losing) is the same as the cost of winning.
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.
