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

In summary, Paul and his friend Peter are playing a coin tossing game where Paul gives Peter a dollar if the coin lands on heads and Peter gives Paul a dollar if it lands on tails. Paul plays the game ten times. The expected total earnings for Paul would be $5, since there is a 50% chance of getting heads or tails on each flip. The variance of Paul's total earnings would be $5, since the outcomes are equally likely. If the coin is biased and Paul has a 0.4 chance of winning for each flip, the expected total earnings would be $4 and the variance would still be $5. This calculation is based on the expected number of tails, which would be 4 out of
  • #1
dream2rule9
1
0
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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  • #2
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
 

1. What is the probability of getting heads on a single coin flip?

The probability of getting heads on a single coin flip is 50%, or 1/2. This is because there are only two possible outcomes (heads or tails) and they are equally likely to occur.

2. What is the probability of getting tails on a single coin flip?

The probability of getting tails on a single coin flip is also 50%, or 1/2. This is because, as mentioned before, there are only two possible outcomes and they are equally likely to occur.

3. What is the probability of getting heads on two consecutive coin flips?

The probability of getting heads on two consecutive coin flips is 25%, or 1/4. This is because each coin flip is an independent event, and the probability of getting heads on each flip is 50%. To calculate the probability of two independent events occurring, you multiply their individual probabilities together (0.5 x 0.5 = 0.25).

4. What is the probability of getting at least one head in two coin flips?

The probability of getting at least one head in two coin flips is 75%, or 3/4. This can be calculated by subtracting the probability of getting no heads (0.25) from 1 (1 - 0.25 = 0.75).

5. Can the probability of getting heads on a coin flip be greater than 50%?

No, the probability of getting heads on a coin flip cannot be greater than 50%. This is because there are only two possible outcomes and they are equally likely to occur, so the probability for each outcome must be equal (50%).

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