The problem here:
2. In eight tosses of a fair coin, find the probability that heads will come up
(a) exactly three times;
(b) at least three times;
(c) at most three times.
Answers:
A)
To solve this part i used next formula:
Where:
- "k" is the number of hits.
- "n" is the number of trials.
- "p" is the probability of success
B)
To solve this part i used next formula
- "k" is the number of hits.
- "n" is the number of trials.
- "p" is the probability of succes
- "u" is the exactly k succes (sigma)
now resolve:
=
=
and the result is: 2.2226
C)
To resolve this part i used the next formula:
Where:
- P is probability of the event,
- C (n, k) are combinations of k elements from n elements a total
- p is the probability of success and q = (1-p) the probability of failure
- n number of times to repeat the individual case
- k number of successes
and the result is:1/256