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scZoUnD [109]
3 years ago
7

From a group of 10 children, a team of 5 (the red team) is randonnly chosen. The remaining 5 children

Mathematics
1 answer:
ivanzaharov [21]3 years ago
6 0

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.

--------------------

  • A probability is the <u>number of desired outcomes divided by the number of total outcomes.</u>
  • 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.

--------------------

<u>Combination formula: </u>

C_{n,x} is the number of different combinations of<u> x objects from a set of n elements</u>, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

--------------------

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.

D = 2C_{8,3} = 2\frac{8!}{3!5!} = 112

--------------------

Finding the number of total outcomes:

  • <u>5 children from a set of 10</u>, thus:

T = C_{10,5} = \frac{10!}{5!5!} = 252

--------------------

The probability is:

p = \frac{D}{T} = \frac{112}{252} = 0.4444

0.4444 = 44.44% probability  they get to be on the same team.

A similar problem is given at brainly.com/question/22931444

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