Question

giving a test to a group of students, the grades and major (stem=science, technology, engineering & mathematics) are summarized below

	a	b	c	total
non - stem majors	3	18	8	29
total	16	25	25	66

if one student is chosen at random, find the probability that the student was stem major or got a(n) \c\.
give your answer as a fraction or decimal out to at least 4 places.

Explanation:

Step1: Recall the formula for $P(A\cup B)$

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$
Let $A$ be the event that the student is a STEM - major and $B$ be the event that the student got a "C".

Step2: Calculate $P(A)$

The number of STEM - majors is $n(A)=37$, and the total number of students is $n = 66$. So $P(A)=\frac{37}{66}$.

Step3: Calculate $P(B)$

The number of students who got a "C" is $n(B)=25$, so $P(B)=\frac{25}{66}$.

Step4: Calculate $P(A\cap B)$

The number of STEM - majors who got a "C" is $n(A\cap B)=17$, so $P(A\cap B)=\frac{17}{66}$.

Step5: Calculate $P(A\cup B)$

$P(A\cup B)=\frac{37}{66}+\frac{25}{66}-\frac{17}{66}=\frac{37 + 25-17}{66}=\frac{45}{66}\approx0.6818$

Answer:

$\frac{45}{66}\approx0.6818$