Can someone please answer this probability question based on coin flip?

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    Coin flip Probability
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SUMMARY

In the discussed probability scenario, Paul plays a coin toss game with Peter, where the expected total earnings for Paul after ten flips is calculated based on a fair coin (0.5 probability). The expected earnings amount to zero, as the game is symmetric. When considering a biased coin with a 0.4 probability of winning (tails), the expected total earnings shift to a loss of $2, while the variance of Paul's total earnings is calculated as 10 times the variance of a single flip, resulting in a variance of 2.4 for the biased scenario.

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Paul is playing a game with his friend Peter where Paul tosses a coin and if it comes up heads
Paul gives Peter a dollar and if it comes up tails Peter gives Paul a dollar. Paul plays the
game ten times.
a. What is the expected total earnings for Paul?
b. What is the variance of Paul's total earnings?
c. Suppose that the dice is biased and Paul has a 0.4 chance of winning for each flip.
repeat the calculations in parts a and b?
 
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Do you know how to calculate expectation values? If so, just calculate the expected number of tails. Then do the same, but instead of a 0.5 probability of tails, its now 0.4
 

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