A box contains 10 red balls and 30 blue balls. Balls will be pulled ou

Question

A box contains 10 red balls and 30 blue balls. Balls will be pulled out of the box and then put back. It will stop when 2 blue balls have been pulled out of the box. What is the probability of getting at least 1 red ball before stopping?

A. 1/2
B. 2/3
C. 9/16
D. 3/4
E. 7/16

A. 1/2
B. 2/3
C. 9/16
D. 3/4
E. 7/16

BrentGMATPrepNow · Accepted Answer

We want P(at least 1 red ball before stopping)
When it comes to probability questions involving  at least , it's best to try using the  complement . 
That is, P(Event A happening) = 1 - P(Event A  not  happening)

So, here we get: P(at least 1 red ball before stopping) = 1 -  P(NO red balls before stopping) 
In other words, P(at least 1 red ball before stopping) = 1 -  P(blue balls only)

P(blue balls only)  
P(blue balls only) = P(1st ball is blue   AND   2nd ball is blue)
= P(1st ball is blue)   x   P(2nd ball is blue)
= 30/40   x   30/40
= 3/4   x   3/4
=  9/16

So, P(at least 1 red ball before stopping) = 1 -  9/16 
= 7/16

Answer: E

Cheers,
Brent

Archit3110 · Answer

P getting 2 blue balls ; 30/40 * 30/40 ; 9/16
and atleast 1 red ; 1-9/16 ; 7/16
IMO E

13swiftness · Answer

there is a vague statement here: will they select the two balls and then put them inside again or pull one ball and then put it back in and then select the second ball. which of the two scenarios? judging from the answer it seems like the second option

SHADOW53 · Answer

When direct calculation seems cumbersome, the best way to find the probability of event A happening is to find the probability of event A not happening.

Probability of Event A (getting at least one red ball) depends on the Probability of event B (drawing two blue balls). 
So, 
 Probability of Event A = 1 - Probability of Event B

Where, 
Probability of Event B =  \frac{ Drawing one blue ball }{ Total number of balls}  *  \frac{ Drawing one blue ball }{ Total number of balls}

Probability of Event B =  \frac{ 30}{40 }  *  \frac{ 30}{40 }  
Probability of Event B =  \frac{90}{160}  or  \frac{9}{16} , when simplified.
Then, 
Probability of Event A = 1 -  \frac{9}{16}  
 Probability of Event A =  \frac{7}{16}

A box contains 10 red balls and 30 blue balls. Balls will be pulled ou

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A box contains 10 red balls and 30 blue balls. Balls will be pulled ou

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