A bag contains 10 marbles, of which 9 are red and 1 is yell

To find out probability of finding the yellow marble - we can also use 1-P(not finding the yellow marble)
I have approached this question by using values from options.
A) If we take out 4 marbles, then P(not finding the yellow marble) = 9c4/10c4 --> Probability of picking 4 marbles out of 9 red marbles only. --> This will be .6. Thus P(finding yellow marble) = .4
B) If we take out 5 marbles, then P(not finding the yellow marble) = 9c5/10c5 --> Probability of picking 5 marbles out of 9 red marbles only. --> This will be .5. Thus P(finding yellow marble) = .5

Hence, B is the CORRECT answer.

For equal probability of picking red or yellow marble i.e. 50%,
number of red marble = number of yellow marble
number of yellow marble = 1, so removing 8 red marble probability of yellow =50%,
so for >50% probability of yellow marble remove 9 red marbles.
Ans: E 9

In order to have a chance of greater than 50%, the other marbles' number must be lower than the number of yellow marble. Since we have only 1 yellow marble, the only possible less number is 0 meaning that we have to take out all the red marbles.
So the answer is E.

Solution

P( Y) > 50% in after how many marbles are taken out .

Now P(Y) in case we pull 1 marble at random is 1/10 = 10%

Now when 2 Marbles are pulled probability of pulling yellow is given by - ( probability of yellow if we pick yellow in first attempt) or (probability of pulling yellow in the second attempt )so its mathematical expression will be :


First attempt yellow P(y) = 1/10 , second attempt yellow probability (Conditional probability applies)= p(not yellow first ) p( Yellow second ) = 9/10 * 1/9 = 1/10

So probability of getting yellow in 2 attempts = probability of yellow if we pick yellow in first attempt) + (probability of pulling yellow in the second attempt ) = 1/10 +1/10 =2/10 = 20%


By induction we can see that we add 10% Probability with each attempt over first one
So Probability of getting yellow in 3 attempts = 30%

So Probability of getting yellow in 5 attempts =50% and in 6 attempts =60%

Thus when we take minimum 6 balls we can be sure that probability of getting yellow is > 50%

So answer is C ) 6 balls

We want P(Yellow)> 50%, this is possible when Yellows > Reds.

Because there is only 1 yellow marble, we should pick 9 reds to ensure we have greater than 50% chance of picking a yellow.

Option E

Probability of finding 1 yellow marble from 10 marbles = P(y) = 1/10

Question asks us to state 50% chances (probability=1/2) of finding the yellow marble in 'n' picks.

1/10 * n > 1/2
n > 5

Minimum value of n = 6

Ans - Option 'C'

Probability of getting Yellow ball when he takes out 1 ball only= 1/10

Probability of getting yellow ball when he takes out 2 balls=
P(1st ball being yellow)+P(2nd ball being yellow, given 1st is red)
=1/10+ 9/10*1/9
=2/10

Similarly Probability of getting yellow ball when he takes out 3 balls=3/10

Hence to get Probability >0.5 or>5/10, he should take out more than 5 balls.
Answer: C- 6 balls

Posted from my mobile device

The most important catch in this question is that there is no replacement.

We want the probability of finding yellow marble to be greater than 50%
Probability of finding red marble = 9/10
Probability of finding yellow marble = 1/10

Let's consider (A)
Without replacement, if we pick up 4 balls, then probability of finding yellow marble is:
\frac{9}{10} * \frac{8}{9} * \frac{7}{8} * \frac{6}{7}
= 60%

If you try the other options, they wil be equal to or less than 50%
Thus, answer is (A) 4

Now if Ram picks out 6 marbles of red. then left over marbles of red will be 3
left over marbles of yellow would be 1
probability of picking yellow marble is 1/4 = 25%
in case he picks 7
then left over marbles of red = 2 ,yellow = 1
probability of picking yellow = 1/3 = 33%
so ram picks 8 marbles
left over is 1 red and 1 yellow
and when he picks 9th marble
it is possible to have yellow 1/2 => 50%
so ram has to pick 9 marbles to have probability of picking yellow marble greater than 50%

Answer c
lets us pick only red marble and we will do a 1-red Marble probability
9/10*8/9*7/8*6/7*5/6=5/10 now we have reached 50 % anything above that will be the answer so the answer is 6

At 1st draw chance of picking a yellow ball is 1/10 {10%}
2nd draw chances of picking yellow ball{assuming 1st attempt failed} = 1/9 {~11%}
3rd draw chances of picking yellow ball{assuming 2nd also attempt failed} = 1/8 {12.5%}
We observe a pattern as the draws proceed. And we require more than 50% chance

Hence after all red balls are picked we can get more than a 50% chance to get a yellow ball. So at least 9 picks are required

IMO E is the answer

A bag contains 10 marbles, of which 9 are red and 1 is yellow. If Ram wants to pick out marbles at random without putting them back, how
many marbles should Ram plan to pick out in order to have a greater than 50% chance of finding the yellow marble among them?

Let Ram take out 1 marble, if it is red, the probability of getting yellow from the bag will be 1/9, which is less than 50%
Similarly, if he takes out 5 marbles, if all of them are red, the probability of getting yellow from the bag will be 1/5, which is less than 50%

Therefore, he has to take out 9 marbles out of the bag in order to be sure that only 1 marble i e yellow is remaining.
Probability in that case = 100 %, which is greater than 50%

Choice E is the answer

OA is B , ie minimum 5 marbles should be drawn to ensure more than 50 % chance of getting yellow marble.