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## 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

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?

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Mathematics
5 months
2021-08-31T04:54:09+00:00
2021-08-31T04:54:09+00:00 1 Answers
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## Answers ( )

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%