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29 Oct 2017, 10:12
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E
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Two players are to be selected from a football team which consists of 10 football players. Is the probability that both the players chosen will be left backs greater than 50 %?
(1) The probability that both players selected will not be left backs is less than 10 %
(2) More than fifty percent of the players are left backs.
Please give kudos, if u liked my post!
(1) The probability that both players selected will not be left backs is less than 10 %
(2) More than fifty percent of the players are left backs.
Please give kudos, if u liked my post!
29 Oct 2017, 20:09
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souvonik2k
Hi...
A good Q..
So we have to choose 2 out of 10.
(1) The probability that both players selected will not be left backs is less than 10 %
Let there be x non left backs, so prob of choosing both is \(\frac{x}{10}*\frac{x-1}{10}<\frac{10}{100}\)...
So x(x-1)<10....
x =3 or <3 because 4*3=12>10 and 3*2=6<10...
So if x=3, left backs are 10-3=7
Prob =7/10*6/9=42/90<50%
If x=2, prob =8/10*7/9=56/90>50%
So insuff
(2) More than fifty percent of the players are left backs.
Say there are 6 or 7, as seen above itwill be <50%
And above 8,9 or 10, prob will be >50%
Insufficient
Combined..
If it is 7, Ans is NO
If 8,9 or 10, Ans is YES
Insufficient
E
27 Jul 2019, 03:41
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Hi Souvonik,
While attempting word problems, the best strategy to employ is to always break down the question stem. Spending time on the question stem will help you evaluate the statements faster.
Total players= 10
The question asks us whether the probability that both players chosen will be left backs (L) is greater than 50 %
Is P(LL) > 50%
(L/10)((L - 1)/9) > 1/2 -----> L(L - 1) > 45
Now for L(L - 1) to be greater than 45, L has to be greater than or equal to 8
The question can be rephrased to 'Is L >= 8'
Statement 1 : The probability that both players selected will not be left backs (N) is less than 10 %
P(NN) < 10%
(N/10)((N - 1)/9) < 1/10 ----> N <=3 ----> L >= 7
Since L can be 7, 8, 9 or 10, we get both a YES and a NO. Insufficient.
Statement 2 : More than fifty percent of the players are left backs.
L > 5 ----> L can be 6, 7, 8, 9 and 10. Insufficient.
Combining the two statements we get L >=7, so again L can be 7, 8 , 9.... Again we get a YES and a NO. Insufficient.
Answer : E
While attempting word problems, the best strategy to employ is to always break down the question stem. Spending time on the question stem will help you evaluate the statements faster.
Total players= 10
The question asks us whether the probability that both players chosen will be left backs (L) is greater than 50 %
Is P(LL) > 50%
(L/10)((L - 1)/9) > 1/2 -----> L(L - 1) > 45
Now for L(L - 1) to be greater than 45, L has to be greater than or equal to 8
The question can be rephrased to 'Is L >= 8'
Statement 1 : The probability that both players selected will not be left backs (N) is less than 10 %
P(NN) < 10%
(N/10)((N - 1)/9) < 1/10 ----> N <=3 ----> L >= 7
Since L can be 7, 8, 9 or 10, we get both a YES and a NO. Insufficient.
Statement 2 : More than fifty percent of the players are left backs.
L > 5 ----> L can be 6, 7, 8, 9 and 10. Insufficient.
Combining the two statements we get L >=7, so again L can be 7, 8 , 9.... Again we get a YES and a NO. Insufficient.
Answer : E
