Kate and her twin sister

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George7: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Sat Oct 20, 2012 8:48 am

Kate and her twin sister

by George7 » Tue Oct 30, 2012 9:22 pm

This is a problem from an MGMAT guide.
How would you solve it? There are several ways to solve it I'd like to know them all.

"Kate and her twin sister Amy want to be in the same relay-race team. There are 6 girls in the group, and only 4 of them will be placed at random in the team. What is the probability that Kate and Amy will both be on the team?"

Thank you!

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Source: Beat The GMAT — Problem Solving | Tue Oct 30, 2012 9:22 pm

pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pm; Thanked: 158 times; Followed by:21 members

by pemdas » Tue Oct 30, 2012 10:44 pm

George7 wrote:This is a problem from an MGMAT guide.
How would you solve it? There are several ways to solve it I'd like to know them all.

"Kate and her twin sister Amy want to be in the same relay-race team. There are 6 girls in the group, and only 4 of them will be placed at random in the team. What is the probability that Kate and Amy will both be on the team?"

Thank you!

The most important part of this problem is saying that 4 people will be placed at random in the team. This means we are not at all interested in ordered selections and all people placed at random in the team make a whole team, no lead, back-ups, just team of four people. We are having one constraint here - select Kate and Amy first, and consider 1 way Kate or Amy is selected for the team.

Next, we select remaining two people for the team out of four people left, 4C2. Our total selections of four people for the team is 6C4, hence 1*(4C2)/(6C4)=p and p=6/15=2/5

Success doesn't come overnight!

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George7: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Sat Oct 20, 2012 8:48 am

by George7 » Wed Oct 31, 2012 8:29 am

Is this a correct way for solving the problem? Probability of Kate being selected: 4/6, probabilty of Amy then being selected 3/5. Then probability of both being slected = 4/6 x 3/5 = 2/5 .

Thanks