In: Statistics and Probability
For a roll with two dice, the following events are
considered:
A: The sum of eyes is greater than 7.
B: Exactly one of the two numbers is a 5.
C: No 1 is rolled.
a) Calculate the probabilities
P (A), P (B), P (C), P (A ∩ B), P (A ∩ C), P (B ∩ C), P (A ∪ B), P
(A | B), P (A | C), P (C | A), P (B | C).
b) Are events A and B independent or disjoint?
In a hall, there are four machines working independently of each
other, which do not fail within a certain time span with the
probabilities 0.9, 0.95, 0.8 and 0.85, respectively.
Calculate the probability that during this period
a) all four machines work b) no machine works
c) exactly one machine works d) exactly two machines work
e) exactly three machines work f) at least one machine works!
A device consists of 100 independent modules of equal
functionality. Zk be that
Event that the kth group works reliably.
a) What is the probability that the device will work reliably at P
(Zk) = 99%?
b) How big must P (Zk) be, so that P (ZGeraet) = 90%?
From a cancer test are given:
Events: T: test result positive, i. Suspected cancer
K: test subject krebskrank
Probability values: P (T | K) = P (Tc | Kc) = 0.95, P (K) =
1/200
Calculate P (T) and P (K | T) and interpret the results!
The elements of the set - A: The sum of eyes is greater than 7 are
The elements of the set - B: Exactly one of the two numbers is a 5 are
The elements of the set - C: No 1 is rolled
are
a) The probabilities
b)Here . hence A and B are not independent.
Also . Hence A and B are not disjoint.