Question

giving a test to a group of students, the grades and gender are summarized below

	a	b	c	total
female	17	19	14	50
total	30	21	19	70

if one student is chosen at random,

find the probability that the student was female or got an \b\.

question help: video message instructor

Explanation:

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

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$

Step2: Calculate $P(\text{Female})$

The total number of students is $n = 70$, and the number of female students is $n_{\text{Female}}=50$. So $P(\text{Female})=\frac{50}{70}$.

Step3: Calculate $P(\text{B})$

The number of students who got a B is $n_{\text{B}} = 21$. So $P(\text{B})=\frac{21}{70}$.

Step4: Calculate $P(\text{Female}\cap\text{B})$

The number of female students who got a B is $n_{\text{Female}\cap\text{B}}=19$. So $P(\text{Female}\cap\text{B})=\frac{19}{70}$.

Step5: Calculate $P(\text{Female}\cup\text{B})$

$P(\text{Female}\cup\text{B})=\frac{50}{70}+\frac{21}{70}-\frac{19}{70}=\frac{50 + 21- 19}{70}=\frac{52}{70}=\frac{26}{35}$

Answer:

$\frac{26}{35}$