Answered

Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Connect with a community of experts ready to help you find accurate solutions to your questions quickly and efficiently. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

Find the probability that when a couple has ​children, at least one of them is a . ​(Assume that boys and girls are equally​ likely.)

Sagot :

MrRoyal

Answer:

[tex]P(At\ least\ one\ girl) = 0.875[/tex]

Step-by-step explanation:

Given

[tex]n = 3[/tex]

[tex]B \to boys[/tex]

[tex]G \to girls[/tex]

[tex]P(G) = P(B) = 0.5[/tex] --- equal probability

See comment for complete question

Required:

[tex]P(At\ least\ one\ girl)[/tex]

To do this, we make use of complement rule:

[tex]P(At\ least\ one\ girl) = 1 - P(No\ girl)[/tex]

The event that there is no girl out of the 3 children is: B B B

And the probability is:

[tex]P(No\ Girl) = P(B) * P(B) * P(B)[/tex]

[tex]P(No\ Girl) = 0.5*0.5*0.5[/tex]

[tex]P(No\ Girl) = 0.125[/tex]

So:

[tex]P(At\ least\ one\ girl) = 1 - P(No\ girl)[/tex]

[tex]P(At\ least\ one\ girl) = 1 - 0.125[/tex]

[tex]P(At\ least\ one\ girl) = 0.875[/tex]

Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We appreciate your time. Please come back anytime for the latest information and answers to your questions. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.