Question

According to a survey, out of the 297 people in our class, 71 have senior standing (7 or more semesters at UCB), and 226 do not. Among those with senior standing, 53 have declared a major and 18 have not. Among those without senior standing, 69 have declared a major and 157 have not. Suppose we are going to choose a single student at random from the class.

(a) Are the events “drawing someone with senior standing” and “drawing someone who hasn’t declared a major” mutually exclusive?
YES or NO (circle one) and justify your answer:

(b) Are the events “drawing someone with senior standing” and “drawing someone who hasn’t declared a major” independent?
YES or NO (circle one) and justify your answer:

(c) What is the conditional probability that the second student drawn has senior standing, if we know the first student drawn has senior standing?


Answer: _____________


(d) What is the probability that the second student drawn has senior standing, not knowing anything about the first?

Answer: _____________


(e) What is the probability that among the five students, none have senior standing?

Answer: _____________

Answer 1

Dear student, we can provide you with the siolution of 4 sub question at a time.

	senior standing	No senior standing
major	53	69	122
No major	18	157	175
	71	226	297

a) Mutually exclusive are the events that cannot happen at the same time

the answer is NO.

The following mentioned events are not mutually exclusive as there are 18 people that have senior standing and have not declared major.

b) The events are independent of each other if the occurrence of one does not affect the occurrence of others.

Let A be the event of drawing someone with senior standing.

B be the event of drawing someone who hasn't declared a major.

Hence

The following events are not independent events.

c) The required probability is

since we know that the first one is drawn has senior standing

d) We assume that the drawings are random and independent

the required probability is