Question

An urn contains 4 red, 5 green, 6 blue and some yellow balls. If two balls are drawn at random, the probability of getting at least one yellow ball is 17/38. find the yellow balls in the urn.
1.4
3.6
4.10
2.5
5.15​

Answer 1

Answer:

option 5 is the right answer

Answer 2

Answer:

Let number of yellow balls in the urn is x . Now, probabilty of getting at least one yellow ball =1- Probabilty of getting no yellow ball ⇒ Probabilty of getting no yellow ball =1−1738=2138.(A)

Now, total number balls in the urn is 4+5+6+x=15+x . 2 balls can be drawn from the urn in C(15+x,2) ways. And the 2 non-yellow balls can be drawn in C(15,2)

So, probabilty of drawing no yellow balls is C(15,2)C(15+x,2)=2∗105(15+x)(15+x−1)=2138 from (A)

Or, 21(15+x)(14+x)=38∗210⇒(x+14)(x+15)=380⇒x2+29x+210=380⇒x2+29x−170=0⇒(x+34)(x−5)=0⇒x−5=0 Or, x=5 ( since x can't be negative)

Hence, there were 5 yellow balls in the urn.