select the correct answer from the drop - down menu. a box contains shirts in two different colors and two…
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.\n|shirt color|size| | |\n|----|----|----|----|\n| |large|medium|total|\n|red|42|48|90|\n|blue|35|40|75|\n|total|77|88|165|\nfrom the data given in the table, we can infer that\np(shirt is medium and blue) = p(medium shirt)\np(red shirt | large shirt) = p(large shirt)\np(large shirt | red shirt) = p(red shirt)\np(blue shirt | large shirt) = p(blue shirt)
Answer
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:
$P(\text{blue shirt}|\text{large shirt}) = P(\text{blue shirt})$