Question

select the correct answer from the drop - down menu. a box contains shirts in two different colors and two different sizes. the numbers of shirts of each color and size are given in the table.

shirt color	size
red	42	48	90
blue	35	40	75
total	77	88	165

from the data given in the table, we can infer that
p(shirt is medium and blue) = p(medium shirt)
p(red shirt | large shirt) = p(large shirt)
p(large shirt | red shirt) = p(red shirt)
p(blue shirt | large shirt) = p(blue shirt)

Explanation:

Step1: Recall conditional - probability formula

$P(A|B)=\frac{P(A\cap B)}{P(B)}$

Step2: Calculate probabilities

$P(\text{large shirt}|\text{red shirt})=\frac{42}{90}=\frac{7}{15}$, $P(\text{red shirt})=\frac{90}{165}=\frac{6}{11}$; $P(\text{blue shirt}|\text{large shirt})=\frac{35}{77}=\frac{5}{11}$, $P(\text{blue shirt})=\frac{75}{165}=\frac{5}{11}$

Answer:

$P(\text{blue shirt}|\text{large shirt}) = P(\text{blue shirt})$