You are given 4 to 1 odds against tossing 2 tails and in 2 tosses of a fair coin. This means that you win $4 if you succeed and you lose $1 if you fail. Find the expected value(toyou) of the game. Round to nearest cent.

The probabality of winning is .2

the probabality of losing is .8

expected value= .2*4+.8(-1)

Thank you!!

To find the expected value of the game, we need to multiply the probability of winning by the amount won and subtract the probability of losing multiplied by the amount lost.

The probability of tossing 2 tails in 2 tosses of a fair coin can be calculated as follows:
Probability of winning = (Probability of getting a tail) * (Probability of getting a tail)
= (1/2) * (1/2)
= 1/4

The probability of losing is the complement of winning, so:
Probability of losing = 1 - Probability of winning
= 1 - 1/4
= 3/4

The amount won is $4 and the amount lost is $1.

Now, we can calculate the expected value:
Expected value = (Probability of winning * Amount won) - (Probability of losing * Amount lost)
= (1/4 * $4) - (3/4 * $1)
= $1 - $0.75
= $0.25

Therefore, the expected value of the game is $0.25.

To find the expected value for a game, you need to multiply each outcome by its probability and then sum them up. In this case, the probability of tossing 2 tails in 2 tosses of a fair coin can be calculated using basic probability.

In a single coin toss, the probability of getting tails is 1/2 since there are two equally likely outcomes (heads or tails). To find the probability of multiple independent events happening together, you multiply the individual probabilities.

Therefore, the probability of getting 2 tails in 2 tosses is (1/2) * (1/2) = 1/4.

Now, let's calculate the expected value:

If you win, you receive $4, and if you lose, you lose $1.

So, the expected value can be calculated as follows:

Expected Value = (Probability of Winning * Amount Won) + (Probability of Losing * Amount Lost)

Expected Value = (1/4 * $4) + (3/4 * -$1)

Expected Value = $1 - $0.75

Expected Value = $0.25

Therefore, the expected value of the game is $0.25.