Given:
The faces on a number cube are labeled 1,2,2,3,4, and 5.
The number cube is rolled 114 times.
To find:
How many times would you expect the number 2 to appear?
Solution:
We have,
Total outcomes = 1,2,2,3,4, and 5.
Number of total outcomes = 6
Favorable outcomes = 2 and 2
Number of favorable outcomes = 2
The probability of getting 2 is:



Now, the expected number of times when 2 to appear is:



Therefore, the expected number of times is 38.
Exponential Function.

Also the shown graph is a decreasing graph.

The equation above is the equation of the graph that is shown in the picture.
Answer:
a) 8/10
b) 
c) Independent events
Step-by-step explanation:
The given information are;
The proportion of women than carries a mutation of the BRCA gene, P(A) = 1/600
The proportion of women in which the mutation develops breast cancer, P(B) = 8/10
a) The probability that a randomly selected woman will develop breast cancer given that she has a mutation of the BRCA gene is given as follows;
1 × P(B) = 1 × 8/10 = 8/10
b) The probability, P that a randomly selected woman woman will carry the mutation of the BRCA gene and will develop breast cancer is given as follows;
P(A) × P(B) = 1/600×8/10 = 1/750 = 
c) The events are dependent
Given that P(A) × P(B) = P(A∩B), the events of carrying the mutation and developing Breast cancer are independent events.