In a class of 29 students, 20 have a brother and 8 have a sister. There are 3 students who do not have any siblings. What is the probability that a student chosen randomly from the class is an only child?
Question
Question
In a class of 29 students, 20 have a brother and 8 have a sister. There are 3 students who do not have any siblings. What is the probability that a student chosen randomly from the class is an only child?
Answer: 1/4 = 0.25 = 25%
Step-by-step explanation:
Let x be the number of students having both brother and sister.
Brother only is 9-x
Sister only is 16-x
Brother only + sister only + both + neither = 28
(9-x) + (16-x) + x + 7 = 28
32 – x = 28
x = 4
The probability per the diagram is 4/16 = 1/4
Per definition of conditional probability:
prob( brother | sister) = prob ( brother AND sister) / prob ( sister)
= 4/16 = 1/4
1/4 = 0.25 = 25%