Four couples at a dinner party play a board game after the meal. They decide to play as teams of two and to select the teams randomly. All eight people write their names on slips of paper. The slips are thoroughly mixed, then drawn two at a time. How likely is it that every person will be teamed with someone other than the person he or she came to the party with?

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13-11-2019
Mathematics

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Four couples at a dinner party play a board game after the meal. They decide to play as teams of two and to select the teams randomly. All eight people write their names on slips of paper. The slips are thoroughly mixed, then drawn two at a time. How likely is it that every person will be teamed with someone other than the person he or she came to the party with?

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wifilethbridge wifilethbridge · Answer 1 · 2019-11-18T07:38:24+01:00

Answer:

0.29

Step-by-step explanation:

We are given that there are 4 couples i.e. 8 people

They decide to play as teams of two and to select the teams randomly

Now we are asked How likely is it that every person will be teamed with someone other than the person he or she came to the party with

For people 1 , there are 6 options for pairing Since he or she cannot pair with his /her own partner

So, Choices For people 1 will be 6 person

So, Probability that person 1 will be teamed with someone other than the person he or she came to the party with = [tex]\frac{\text{No. of choices for Person 1}}{\text{Total no. of choices available}}=\frac{6}{7}[/tex]

So, Probability that every person (=8 person) will be teamed with someone other than the person he or she came to the party with =[tex](\frac{6}{7})^8=0.29[/tex]

Hence Probability that every person will be teamed with someone other than the person he or she came to the party with is 0.29