Answer: a) 0.40 b) 0.15
Step-by-step explanation:
Let A denotes the event that students wear a watch and B denotes the event that students wear a bracelet.
Given : P(A)=0.25 ; P(B)=0.30
[tex]P(A'\cup B')=0.60[/tex]
Since, [tex]P(A\cup B)=1-P(A'\cup B')=1-0.60=0.40[/tex]
Thus, the probability that this student is wearing a watch or a bracelet = 0.40
Also, [tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]
[tex]P(A\cap B)=P(A)+P(B)-P(A\cup B)[/tex]
[tex]P(A\cap B)=0.25+0.30-0.40\\\\\Rightarrow\ P(A\cap B)=0.15[/tex]
Thus, the probability that this student is wearing both a watch and a bracelet= 0.15
Answer:
Step-by-step explanation:
Given that at a certain school, twenty-five percent of the students wear a watch and thirty percent wear a bracelet.
A- people who wear watch = 25%
B - people who wear bracelet = 30%
(AUB)' - People who wear neither a watch nor a bracelet=60%
[tex]A \bigcap B[/tex] - People who wear both =100%-60% = 40%
a) [tex]P(AUB) = P(A)+P(B)-P(AB) = 25%+30%-40%\\= 15%[/tex]
b) the probability that this student is wearing both a watch and a bracelet
= [tex]P(A \bigcap B) = 40%[/tex]
