Is 1.5 over 7.5 a rational number
1 answer:
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Answer:
Sample space = {(T,T), (T,H), (HT), (HH)}
Step-by-step explanation:
We are given a fair coin which when tossed one times either gives heads(H) or tails(T).
Now, the same coin is tossed two times.
1) All the possible outcomes
Tails followed by tails
Rails followed by heads
Heads followed by a tail
Heads followed by heads
2) Sample space
{(T,T), (T,H), (HT), (HH)}
3) Formula:
Using the above formula, we can compute the following probabilities.
Probability((T,T)) =
Probability((T,H)) =
Probability((H,T)) =
Probability((H, H)) =
Probability(Atleast one tails) =
Probability(Atleast one heads) =
Probability(Exactly one tails) =
Probability(Exactly one heads) =
The Jacobian for this transformation is
with determinant , hence the area element becomes
Then the integral becomes
where is the unit circle,
so that
Now you could evaluate the integral as-is, but it's really much easier to do if we convert to polar coordinates.
Then