Respuesta :
Using the concept of probability and the combination formula, it is found that there is a 0.4444 = 44.44% probability they get to be on the same team.
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- A probability is the number of desired outcomes divided by the number of total outcomes.
- The order in which the children are chosen is not important, which means that the combination formula is used to find the number of outcomes.
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Combination formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
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Finding the number of desired outcomes:
- Andy and Ollie on the same team, plus 3 children from a set of 8.
- Can be on either team, blue or red, so multiplied by 2.
[tex]D = 2C_{8,3} = 2\frac{8!}{3!5!} = 112[/tex]
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Finding the number of total outcomes:
- 5 children from a set of 10, thus:
[tex]T = C_{10,5} = \frac{10!}{5!5!} = 252[/tex]
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The probability is:
[tex]p = \frac{D}{T} = \frac{112}{252} = 0.4444[/tex]
0.4444 = 44.44% probability they get to be on the same team.
A similar problem is given at https://brainly.com/question/22931444
