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There are 20 children in the cast of a class play, and 8 of the children are boys.  Of the boys, 5 have a speaking part in the play, and of the girls, 7 do not have a speaking part in the play.  If a child from the cast of the play is chosen at random, what is the probability that the child has a speaking part?

Sep 17, 2021

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The number of boys 8. Hence, the number of girls is 20 – 8 = 12.

The number of boys, who have a speaking part in the play is 5. Hence, the number of boys, who do not have a speaking part in the play is 8 – 5 = 3.

The number of girls, who do not have a speaking part in the play is 7. Hence, the number of girls, who have a speaking part in the play is 12 – 7 = 5.

Hence, consider the below contingency table:

Gender  Speaking part in play  No speaking part in play  Row Total
Boy          5                                 3                                     8

Girl          5                                 7                                     12

Column Total 10                       10                                     20

The total number of children, who have a speaking part is 10.

Thus, if a child from the cast of the play is chosen at random, the probability that the child has a speaking part is 10/20 = 1/2 = 0.5.

Sep 19, 2021