Question

An urn contains 9 red balls and p green balls. If the probability of picking a red ball is thrice that of picking a green ball, then p is equal to
A.6
B.7
C.2
D.3

Answer 1

Hint: First calculate the probability of picking a red ball and the probability of picking a green ball, then given that the probability of picking a red ball is thrice that of picking a green ball so equating those two equations then we will get the value of p.

Complete step-by-step answer:
The probability of an event A is given by the relation \[P\left( A \right)=\dfrac{\text{Favourable events}}{\text{Total events}}\]
Given that an urn contains 9 red balls and p green balls
The total number of possible outcomes is \[9+p\], these are our total outcomes.
We have that the urn contains 9 red balls; these are our favourable events.
The probability of picking a red ball is \[\dfrac{9}{9+p}\]
The probability of picking a green ball is \[\dfrac{p}{9+p}\]
Given the probability of picking a red ball is thrice that of picking a green ball
\[\dfrac{9}{9+p}=3\left( \dfrac{p}{9+p} \right)\]. . . . . . . . . . . . . . . . . . (1)
\[3p=9\]. . . . . . . . . . . . . . . . . . . . . . . . . . .(2)
\[p=3\]
So, the value we obtained is that p is 3
Therefore we can conclude that the urn contains 3 green balls.
The correct option is option (D).

Note: Probability is the branch of mathematics dealing with how likely an event is to occur. Probability of an event always lies between 0 and 1. We know that the probability is the ratio of total number of desired outcomes to the total number of the possible outcomes. If the value of probability is zero it indicates impossible events and probability 1 indicates certainty of event.