An urn contains 5 red and 2 green balls

Asked by admin @ 23/08/2021 in Math viewed by 312 People

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

Answered by admin @ 23/08/2021

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 $\frac{5}{7}$

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