Respuesta :
The probability that the brother and sister are both selected is 0.5052.
What is probability?
Probability deals with the occurrence of a random event. The chance that a given event will occur. It is the measure of the likelihood of an event to occur.The value is expressed from zero to one.
For the givens situation,
Total number of boys and a brother = 12
Total number of girls and a sister = 8
A brother is included among boys. So among 12 boys anyone can be a brother.
Similarly, a sister is included among girls. So among 8 girls anyone can be a sister.
The probability that the brother and sister are both selected is
⇒ [tex]P(e)=\frac{(12C_{1} )(8C_{1})}{(20C_{2})}[/tex]
we know that [tex]nC_{r} =\frac{n! }{r!(n-r)!}[/tex]
⇒ [tex]12C_{1}=12, 8C_{1} = 8[/tex] and [tex]20C_{2}=190[/tex]
⇒ [tex]P(e)=\frac{(12 )(8)}{190}[/tex]
⇒ [tex]P(e)=\frac{48}{95}[/tex]
⇒ [tex]P(e)=0.5052[/tex]
Hence we can conclude that the probability that the brother and sister are both selected is 0.5052.
Learn more about probability here
https://brainly.com/question/484120
#SPJ2
