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Answer:
Step-by-step explanation:
Given that a contestants have a chance to increase their current winnings of $1 million to $2 million.
Also given that They have a 50% chance of winning. should they play
Thus we have 0.50 chance of getting additional 1 million or
0.50 chance of getting nothing.
Expected value of the gain by playing
=[tex]0.5(1000,000)+0.5(0)\\= 500,000 $[/tex]
Since expected value is positive, they can play and try.
They should play the game because there is a 50% chance of winning the $1 million dollars and 50% chance of losing $500,000
Further explanation
The question is about the Game Show Uncertainty. Probability itself is the number of ways of achieving success / unsuccess
In the final round of a TV game show, contestants have the chance to increase their current winnings of $1 million dollars to $2 million dollars. They have a 50% chance of winning. Should they play?
There is a 50% chance of winning the $1 million dollars, also 50% chance of losing $500,000.
[tex]1,000,000*0.5 = 500,000\\0.5*1,000,000 + 0.5*-500,000 = $250,000[/tex]
The other problem is:
It costs $1 million to play
if you are right, you win $2 million. Whereas if you are wrong, you win $500,000.
The expected value of playing is $1 million.
[tex]0.5*2000000 + 0.5*500000)= 1,250,000[/tex]$
$ 1,250,000 is higher than the cost of playing
The minimum probability of a guess to make the playing still profitable is 33%
[tex]33.3*1.000.000*(x) + (-500.000)(1-x)[/tex]
[tex]1.000.000*x -500.000 + 500.000*x[/tex]
[tex]1.500.000*x = 500.000*X[/tex]
[tex]\frac{500.000}{1.500.000}*X[/tex]
[tex]\frac{1}{3}= 33.3[/tex]%
Learn more
- Learn more about probability https://brainly.com/question/7965468
- Learn more about chance https://brainly.com/question/4325848
- Learn more about winnings https://brainly.com/question/2146500
Answer details
Grade: 5
Subject: Math
Chapter: probability
Keywords: probability, chance, winnings, play, contestants
