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Maths Probability

Dear all, I was doing a question and did not understand why my working was incorrect. If anyone would be so kind as to clarify a doubt i have, I would greatly appreciate it!

Question: In a badminton team of 8 players, 5 are boys and 3 are girls. Boy A and Girl B are the only 2 left handed players in the team. In a particular practice, 4 players are chosen to play doubles. Find the probability that exactly 1 left handed player is chosen.

The answer for this is 4/7 but my working was:
P( 1 left handed player) = P(Boy A and no girl B)+ P(Girl B and no boy A)
= (1/8)(6/7)(5/6)(4/5) + (1/8)(6/7)(5/6)(4/5) = 1/7
Is it necessary to multiple a 4 here because of the ways to permutate left-handed person and 3 right-handed people? So it would be 4!/3!

Thank you so much!
I don’t really understand your method so I don’t know if it would work for all probability problems like this one but statistics has never been my strongest area in maths.

I would make p(L) probably of left handed and p(R) probability of right handed.
Possible combinations are RRRL, LRRR, RLRR RRLR. I would draw a tree diagram and work out the probability of each of these combinations which is 1/7 for each this reaches the answer of 4/7.
Original post by thebluhood
Dear all, I was doing a question and did not understand why my working was incorrect. If anyone would be so kind as to clarify a doubt i have, I would greatly appreciate it!

Question: In a badminton team of 8 players, 5 are boys and 3 are girls. Boy A and Girl B are the only 2 left handed players in the team. In a particular practice, 4 players are chosen to play doubles. Find the probability that exactly 1 left handed player is chosen.

The answer for this is 4/7 but my working was:
P( 1 left handed player) = P(Boy A and no girl B)+ P(Girl B and no boy A)
= (1/8)(6/7)(5/6)(4/5) + (1/8)(6/7)(5/6)(4/5) = 1/7
Is it necessary to multiple a 4 here because of the ways to permutate left-handed person and 3 right-handed people? So it would be 4!/3!

Thank you so much!

The question is not entirely clear about the type of doubles.
There are three types of doubles categories:-
Male doubles
Female doubles
Mixed doubles (one male/one female as a pair)


Since there are only 3 girls, female doubles isn't possible.

For a male doubles match, 4 of the 5 boys are selected, so the chance of getting the 1 left-handed boy is 4/5.

For mixed doubles, 2 boys and 2 girls are required. The chance of getting a left-handed boy is 2/5. The chance of getting a left-handed girl is 2/3.
The chance of getting either a left-handed boy or a left-handed girl but not both is:
2/5 × 1/3 + 2/3 × 3/5 = 8/15

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