Question 5 The half-life of iodine-131 is 8 days. The amount of a 100 gram
sample of the isotope left d days after being introduced is
I = 100 (½)^d/8
What is the percent change per day?

A. 8.3% decrease per day
B. 91.7% decrease per day
C. 50% decrease per day
D. 99.6% decrease per day

Step-by-step explanation:

a) Two events A,B are said to be mutually exlusive if any of the following occurs.

- A and B have an empty intersection

- A= B^c and their union is the whole sample space

- P(A intersection B) =0

REcall the following formula

Note that P(A) + P(B) = 1.1. Since the probability is always a number between 0 and 1, it must happen that , otherwise, would have a probability greater than 1. Hence, A, B are not mutually exclusive.

b) by definition, if two events are indepent, we have that the probability of the intersection is equal to products of their probabilites. Or

c) Recall that if we have mutuallly exclusive events A, B, then we have that  , if they were independent, we would have the following

which necesarilly implies that at least one of the two events has 0 probability. (THis is not the case)