If a point is randomly selected within the larger circle, the chance that it also lies within the smaller circle is 0.25. Step-by-step explanation: i) The area of the smaller circle is calculated as

=

. ii) The area of the larger circle is given by 
. iii) The likelihood that a randomly selected point from the larger circle also resides in the smaller circle is expressed as 
.
Answer:
a) P=0.24
b) P=0.31
c) Not independent.
Step-by-step explanation:
The question is incomplete.
a) What’s the probability that a randomly chosen order will be wrapped and sent to a different person?

W: wrapped
SOP: sent to different individuals
b) What’s the probability that a randomly selected order will be gift wrapped?

SR: sent to the correct recipient
c) Is gift wrapping independent of the order’s destination? Please provide a statistical justification.
To establish their independence, both conditions must be satisfied:
- P(x|y) = P(x), for all values of X and Y.
- P(x ∩ y) = P(x) * P(y), for all values of X and Y.
Starting with the second condition.

This condition is unmet, indicating that these variables are not independent.