Question

Jimmy tosses an unbiased coin two times in succession. He wins $1 for heads on the first toss, $2 for heads on the second toss. For each tail on a
toss he looses $1. Let X denote Jimmy's earning. Find P(X>0)​

Answer 1

Answer:

If we flip a coin 30 times, with every head winning 5 dollars and for every tail losing 4 dollars. What is the expected value E(W) of W, with W being the random variable amount of money you would win.

What I think it is:

E(W)=30⋅51230+30⋅(−4)1230

Does this seem correct

Answer 2

Answer: Probability of Jimmy's earning greater than zero is 0.5

Explanation:

Ways in which Jimmy will win money are as follows :

1. Heads on both first and second toss
2. Tails on first toss and heads on second toss

Probability of case 1 : Probability of heads on first toss × Probability of heads on second toss =  $\frac{1}{2} * \frac{1}{2}$  = 1/4

Probability of case 2 : Probability of tails on first toss × Probability of heads on second toss =  $\frac{1}{2} * \frac{1}{2}$  = 1/4

Net probability of Jimmy winning = $\frac{1}{4} + \frac{1}{4} = \frac{1}{2}$

#SPJ3