| Author |
Message |
|
rrampriya
|
Post subject: A certain basket contains 10 apples - Probability question  Posted: Thu Sep 09, 2010 5:12 pm |
|
 |
| Course Students |
|
|
Posts: 4
|
|
A certain basket contains 10 apples, 7 of which are red and 3 are green. If 3 different apples are to be selected at random from the basket, what is the probability that 2 of the apples selected will be red and 1 will be green?
a) 7/40
b) 7/20
c) 49/100
d) 21/40
e) 7/10
Can someone help to solve this problem?
|
|
  |
|
 |
|
gokul_nair1984
|
Post subject: Re: A certain basket contains 10 apples - Probability question Posted: Fri Sep 10, 2010 2:12 am |
|
|
| Students |
|
|
Posts: 170
|
rrampriya wrote: A certain basket contains 10 apples, 7 of which are red and 3 are green. If 3 different apples are to be selected at random from the basket, what is the probability that 2 of the apples selected will be red and 1 will be green? 7 Red+ 3 Green=10 Apples Probability that 2 of the apples selected will be red means selecting 2 red apples from 7 red ones. This can be mathematically stated as 7C2 or C(7,2)------(1)Similarly, Probability of selecting 1 green apple from 3 green ones can be mathematically stated as 3C1 or C(3,1)----(2)In Totality you are selecting 3 apples from a group of 10 which can be stated as 10C3 or C(10,3)----(3)So the combined probablity can be expressed as
[C(7,2)*C(3,1)]/C(10,3) and this simplifies to 21/40
|
|
| |
|
|
|
RonPurewal
|
Post subject: Re: A certain basket contains 10 apples - Probability question Posted: Thu Sep 16, 2010 7:48 am |
|
|
| ManhattanGMAT Staff |
|
|
Posts: 6765
|
gokul_nair1984 wrote: rrampriya wrote: A certain basket contains 10 apples, 7 of which are red and 3 are green. If 3 different apples are to be selected at random from the basket, what is the probability that 2 of the apples selected will be red and 1 will be green? 7 Red+ 3 Green=10 Apples Probability that 2 of the apples selected will be red means selecting 2 red apples from 7 red ones. This can be mathematically stated as 7C2 or C(7,2)------(1)Similarly, Probability of selecting 1 green apple from 3 green ones can be mathematically stated as 3C1 or C(3,1)----(2)In Totality you are selecting 3 apples from a group of 10 which can be stated as 10C3 or C(10,3)----(3)So the combined probablity can be expressed as
[C(7,2)*C(3,1)]/C(10,3) and this simplifies to 21/40nicely done.
|
|
| |
|
|
|
aaron.1choi
|
Post subject: Re: A certain basket contains 10 apples - Probability question Posted: Mon Aug 29, 2011 11:29 am |
|
|
| Students |
|
|
Posts: 7
|
|
I did it a different way.
First: calculate all possible ways to choose 3 apples from 10.
10x9x8 = 720
Second: calculate the number of ways 2 green and 1 red ball can be chosen.
(ways to choose 1st green ball) x (ways to choose 2nd green ball) x (ways to choose 1st red ball)
7C2 x 6C1 x 3C1
= (7!)/(2!5!)x(6!)/(1!5!)x(3!)/(1!2!) = ((7x6)/2)x6x3 = 378
probability of 2G1R combination = number ways for 2G1R/total ways
=378/720
=21/40
|
|
| |
|
|
|
RonPurewal
|
Post subject: Re: A certain basket contains 10 apples - Probability question Posted: Sat Sep 03, 2011 9:21 pm |
|
|
| ManhattanGMAT Staff |
|
|
Posts: 6765
|
|
that works too.
is this problem actually from the GMAT PREP software?
|
|
| |
|
|
|
dudewheysmehemail
|
Post subject: Re: A certain basket contains 10 apples - Probability question Posted: Thu Sep 08, 2011 10:47 pm |
|
|
| Students |
|
|
Posts: 4
|
RonPurewal wrote: that works too.
is this problem actually from the GMAT PREP software? Hi Ron, Yes this question is from the GMAT Prep test software. I took Practice Test Two today and I got it. Unfortunately my answer was wrong :-( I was running short of time and this came up as #34, so I tried to rush through it and made an educated guess. I tried: 2 red apples and 1 green apple = 7/10 * 6/9 * 3/8 = 7/40. I understand the other approaches listed above, but in this approach, I guess I didn't account for the 3 ways that this can happen (7/40 * 3 = 21/40). Is this the right logic? Many thanks! --Rishi
|
|
| |
|
|
|
mithunsam
|
Post subject: Re: A certain basket contains 10 apples - Probability question Posted: Fri Sep 09, 2011 10:35 am |
|
|
| Course Students |
|
|
Posts: 76
|
dudewheysmehemail wrote: RonPurewal wrote: that works too.
is this problem actually from the GMAT PREP software? Hi Ron, Yes this question is from the GMAT Prep test software. I took Practice Test Two today and I got it. Unfortunately my answer was wrong :-( I was running short of time and this came up as #34, so I tried to rush through it and made an educated guess. I tried: 2 red apples and 1 green apple = 7/10 * 6/9 * 3/8 = 7/40. I understand the other approaches listed above, but in this approach, I guess I didn't account for the 3 ways that this can happen (7/40 * 3 = 21/40). Is this the right logic? Many thanks! --Rishi That is correct. 7/10 * 6/9 * 3/8 gives us the scenario of picking two red balls first, then a green ball (RRG). Other possibilities are GRR and RGR. Therefore, we need to multiply with 3.
|
|
| |
|
|
|
RonPurewal
|
Post subject: Re: A certain basket contains 10 apples - Probability question Posted: Mon Sep 12, 2011 4:11 am |
|
|
| ManhattanGMAT Staff |
|
|
Posts: 6765
|
mithunsam wrote: 7/10 * 6/9 * 3/8 gives us the scenario of picking two red balls first, then a green ball (RRG). Other possibilities are GRR and RGR. Therefore, we need to multiply with 3. yep
|
|
| |
|
|
|
