Question

An urn contains 5 red balls and 2 green balls. two balls are drawn one after the other.what is the probability that the second ball is red

Answer 1

The urn contains 7 balls.
The probability of the first ball being red is 5/7
and the ball being green is 2/7

After the first ball is drawn, the total number of ball still inside the urn is 6

case 1:-
If the first ball was red then the probabilities change to:-
A red ball next time 4/6 => 2/3
A green ball next time 2/6 => 1/3

case 2:-
If the first ball was green then the probabilities change to:-
A red ball next time 5/6
A green ball next time 1/6


Therefore you have two answers
according to case 1: the answer is 2/3
according to case 2: the answer is 5/6.

Answer 2

Answer:

The probability that the second ball is red is $\frac{5}{7}$

Step-by-step explanation:

Given : An urn contains 5 red balls and 2 green balls. Two balls are drawn one after the other.

To find : What is the probability that the second ball is red ?

Solution :

Number of red balls = 5

number of green balls = 2

Total number of balls = 7

There are two possibilities :

1) If the first ball was red and second ball is also red.

The probability is $\frac{5}{7}\times \frac{4}{6}=\frac{20}{42}$

2) If the first ball was green and second ball is red.

The probability is $\frac{2}{7}\times \frac{5}{6}=\frac{10}{42}$

The probability that the second ball is red is given as

$P=\frac{20}{42}+\frac{10}{42}$

$P=\frac{30}{42}$

$P=\frac{5}{7}$

Therefore, The probability that the second ball is red is $\frac{5}{7}$