If the odds are 3 to 5 in favor of man receiving $200 if a certain act is performed, find his mathematical expectation.
If the odds are 3 to 5 in favor, this means that the man will get the $200 3 times out of 3+5 times, or 3 out of 8, which is .375, or 37.5% of the time. ☺☺☺☺
Well, to calculate his mathematical expectation, we simply have to multiply the probability of each outcome by its corresponding gain or loss.
So, in this case, the probability of him receiving $200 is 3/8 (3 favorable outcomes out of 8 total outcomes). And the gain is $200.
Now, the probability of him not receiving anything is 5/8 (5 unfavorable outcomes out of 8 total outcomes). And the gain in this case is $0.
So, we multiply the probability of each outcome by its gain and add them up:
Expected gain = (3/8) * $200 + (5/8) * $0
= $600/8
= $75
So, his mathematical expectation is $75. But keep in mind, the real-life expectation might be different because the world is unpredictable, just like my jokes!
To find the mathematical expectation, we need to multiply the probability of each outcome by the respective outcome and sum them up.
In this case, the odds are given as 3 to 5 in favor of the man receiving $200. This means that for every 3 favorable outcomes, there are 5 unfavorable outcomes.
Let's calculate the probability of the man receiving $200:
Probability of receiving $200 = Number of favorable outcomes / Total number of possible outcomes
Probability of receiving $200 = 3 / (3 + 5) = 3/8
Now let's calculate the expected value:
Expected value = (Probability of receiving $200) * ($200) + (Probability of not receiving $200) * ($0)
Expected value = (3/8) * $200 + (5/8) * $0
Expected value = $75
Therefore, the man's mathematical expectation is $75.
To find the mathematical expectation, we need to multiply each possible outcome by its corresponding probability and then sum up these values. In this case, the odds are given as 3 to 5 in favor of the man receiving $200.
Let's break down the given odds. The "3 to 5" odds can be written as a fraction, where the numerator represents the favorable outcomes (in this case, the man receiving $200) and the denominator represents the total possible outcomes.
The fraction can be written as 3/5, which means that out of 8 total outcomes, 3 are favorable and 5 are not.
To calculate the mathematical expectation, we multiply the value of each outcome by its probability:
Expected Value = (Probability of Outcome 1 × Value of Outcome 1) + (Probability of Outcome 2 × Value of Outcome 2) + ...
In this case, there are two possible outcomes:
Outcome 1: The man receives $200 (favorable outcome)
Outcome 2: The man receives nothing (unfavorable outcome)
Let's assign the respective values to these outcomes:
Outcome 1: Value = $200
Outcome 2: Value = $0
Now, we need to determine the probability of each outcome. Since the odds are 3 to 5 in favor of the man receiving $200, we can calculate the probabilities as follows:
Probability of Outcome 1 (man receiving $200) = Favorable outcomes / Total outcomes = 3 / 8
Probability of Outcome 2 (man receiving nothing) = Unfavorable outcomes / Total outcomes = 5 / 8
Now, we can calculate the mathematical expectation:
Expected Value = (Probability of Outcome 1 × Value of Outcome 1) + (Probability of Outcome 2 × Value of Outcome 2)
Expected Value = [(3/8) × $200] + [(5/8) × $0]
Expected Value = ($600/8) + ($0/8)
Expected Value = $75
Therefore, the mathematical expectation for the man is $75.