Question

a contestants have a chance to increase their current winnings of $1 million to $2 million. They have a 50% chance of winning. should they play?

Answer 1

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

=$0.5(1000,000)+0.5(0)\\= 500,000$

Since expected value is positive, they can play and try.

Answer 2

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.

$1,000,000*0.5 = 500,000\\0.5*1,000,000 + 0.5*-500,000 = 250,000$

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.

$0.5*2000000 + 0.5*500000)= 1,250,000$$

$ 1,250,000 is higher than the cost of playing

The minimum probability of a guess to make the playing still profitable is 33%

$33.3*1.000.000*(x) + (-500.000)(1-x)$

$1.000.000*x -500.000 + 500.000*x$

$1.500.000*x = 500.000*X$

$\frac{500.000}{1.500.000}*X$

$\frac{1}{3}= 33.3$%

Learn more

1. Learn more about probability brainly.com/question/7965468
2. Learn more about chance brainly.com/question/4325848
3. Learn more about winnings brainly.com/question/2146500

Answer details

Grade:        5

Subject:  Math

Chapter:  probability

Keywords:  probability, chance,  winnings, play, contestants