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Assume that male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children. Find the probability of exactly nine boys in ten births. Round the answer to the nearest thousandth.

Respuesta :

Answer:

P(9 boys/10births)= approx 0.01

Step-by-step explanation:

Lets indicate the BOY=B and the GIRL=G

We investigate the case of 10 kids births.

That means that each possible outcome of the event is looking like that:

X-X-X-X-X-X-X-X-X-X

In each position of X letter can be as letter B  as letter G (2 possible options).

So the total amount of the outcomes is 2^10  =1024

The number of the outcomes where the amount of letter B =9 is 10.

(the outcomes are as follows)

1).  G BBB BBB BBB

2)  B GBB BBB BBB

3). B BGB BBB BBB  

4). B BBG BBB BBB

5). B BBB GBB BBB

6) B BBB BGB BBB

7) B BBB BBG BBB

8) B BBB BBB GBB

9) B BBB BBB BGB

10) B BBB BBB BBG

Or we can calculate it from formulae A10(9)= 10!/9! =10

So the probability of 9 boys in ten births is

P(9Boys/10)= 10/1024=0.009765625= approx. 0.01

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