Answer:
The probability that the student is right-handed given that the student is a girl is:
[tex]\dfrac{5}{6}[/tex]
Step-by-step explanation:
From the tree diagram we have to find the probability that the students is right handed given that the student is a girl.
Let A denote the event that the student is a girl.
and B denote the event that the student is right handed.
We are asked to find the probability:
P(B|A)
We know that P(B|A) is calculated as:
[tex]P(B|A)=\dfrac{P(A\bigcap B)}{P(A)}[/tex]
There are a total of 500 students.
Out of which 300 are girls.
( i.e. [tex]P(A)=\dfrac{300}{500}=\dfrac{3}{5}[/tex] )
and out of 300 girls 250 are right handed.
( i.e. [tex]P(A\bigcap B)=\dfrac{250}{500}=\dfrac{1}{2}[/tex] )
Hence,
[tex]P(B|A)=\dfrac{\dfrac{1}{2}}{\dfrac{3}{5}}\\\\\\P(B|A)=\dfrac{5}{6}[/tex]
Hence,The probability that the student is right-handed given that the student is a girl is:
[tex]\dfrac{5}{6}[/tex]
