Plz help on these two.
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Answer:
Check the explanation
Step-by-step explanation:
The odds are 4 to 1 against, so we can estimate the probability of success (p) as
The expected pay for every success is 3 to 1, so we lose $1 for every lose and we gain $3 for every win.
The number of winnings in the 100 rounds to be even can be calculated as:
We have to win at least 25 rounds to have a positive payoff.
As the number of rounds is big, we will approximate the binomial distribution to a normal distribution with parameters:
The z-value for x=25 is
The probability of z>1.25 is
P(X>25)=P(z>1.25)=0.10565
There is a 10.5% chance of having a positive payoff.
NOTE: if we do all the calculations for the binomial distribution, the chances of having a net payoff are 13.1%.