Question

In the final round of a TV game show, contestants have a chance to increase their current winnings of $1 million to $2 million. If they are wrong, their prize is decreased to $500,000. A contestant thinks his guess will be right 50% of the time. Should he play? What is the lowest probability of a correct guess that would make playing profitable?

They should play because the payoff will be positive.

.50 X 1,00,000 = 500,000 Total gain if you win

.50 X 500,000 = 250,000 Total loss if you lose

.5 X 1,000,000 + .5 X -500,000= 250,000

So the expected value of playing 1 million is $1,250,000

p1,000,000 + (-500,000) + p500,000

=p1,500,000 - 5000,000

500,000 = p1,500,000

1,500,000 1,500,000

⅓ or 33%

I can do the math once given the equation but I am not understanding why I should use the equation.

Answer #1

If Contestants Wins,

They will earn $ 1,000,000 and If They take wrong decision,

They will loose $500, 000.

Probability of Winning And Loosing is 0.50 Therefore,

0.50 X (+ 1000,000) =$500, 000

0.50 X (- 500,000) =$250, 000

While, Taking in to account the probability of winning and losing,

We can see that Contestants have 50% chance of winning $ 500,000 and 50% chance of losing $250,000. So, Contestants should play. If probability of loss is greater than the probability of winning then, Contestants should not play.

If probability of winning will be 25% then,

Contestants earn,

0.25 X (+ 1000,000) = $ 250,000 which is equal to the losing of amount.

So, Lowest Probability of a correct guess that make Contestants profitable is 26%.

When Probability is 26% then participants wins: 0.26 X(+ 1000,000) =$260, 000

17-2
Game Show Uncertainty In the final round of a TV game show,
contest ant shave a chance to increase their current winnings of$1
million to $2 million. If they are wrong, their prize is decreased
to $500,000. A contestant thinks his guess will be right 50% of the
time. Should he play? What is the lowest probability of a correct
guess that would make playing profitable?

You're a contestant on a TV game show. In the final round of the
game, if contestants answer a question correctly, they will
increase their current winnings of $1 million to $3 million. If
they are wrong, their prize is decreased to $750,000. You believe
you have a 25% chance of answering the question correctly.
Ignoring your current winnings, your expected
payoff from playing the final round of the game
show is?
Given that this is (positive, negative), you
(should,...

You're a contestant on a TV game show. In the final round of the
game, if contestants answer a question correctly, they will
increase their current winnings of $3 million to $4 million. If
they are wrong, their prize is decreased to $2,250,000. You believe
you have a 25% chance of answering the question correctly. Ignoring
your current winnings, your expected payoff from playing the final
round of the game show is $ . Given that this is , you...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 33 minutes ago

asked 36 minutes ago

asked 36 minutes ago

asked 38 minutes ago

asked 41 minutes ago

asked 48 minutes ago

asked 56 minutes ago

asked 59 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago