Question

a random sample of 114 statistics students were asked about their latest test score (pass or fail) and whether they studied for the test or not. the following contingency table gives the two - way classification of their responses.

	pass	fail
did not study	39	10

suppose one student is randomly selected from the group. calculate the following probabilities.
round solutions to three decimal places, if necessary.
p(did study and pass)=0.325
p(did not study and fail)=0.088
p(pass or did not study)=0.754
p(fail or did study)=0.754
p(fail and pass)=
p(pass or fail)=

Explanation:

Step1: Understand mutually - exclusive events

A student cannot both pass and fail a test simultaneously. So, the event of failing and passing is a mutually - exclusive event.

Step2: Calculate probability of mutually - exclusive event

For mutually - exclusive events $A$ and $B$, $P(A\cap B)=0$. So, $P(\text{Fail and Pass}) = 0$.

Step3: Calculate $P(\text{Pass or Fail})$

The events of passing and failing a test are complementary events. For complementary events $A$ and $B$, $P(A\cup B)=P(A)+P(B)$. Since a student either passes or fails (no other options in this context), $P(\text{Pass or Fail}) = 1$.

Answer:

$P(\text{Fail and Pass}) = 0$
$P(\text{Pass or Fail}) = 1$