Question

There are two bags, one bag contains 5 white and 10 red balls. The other contains 10 white and 7 red balls. What is the probability taking a red ball from one of the bags ?

Answer 1

Answer

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Answer 2

Answer: Probability of taking red ball from one of the bags is $\dfrac{55}{102}$

Step-by-step explanation:

Since we have given that

There are two bags:

Probability of choosing one bag = $\dfrac{1}{2}$

Probability of choosing another bag =  $\dfrac{1}{2}$

Number of white balls in first bag = 5

Number of red balls in first bag = 10

Number of white balls in second bag = 10

Number of red balls in second bag = 7

So, probability of taking a red ball from one of the bags is given by

$\dfrac{10}{15}\times \dfrac{1}{2}+\dfrac{1}{2}\times \dfrac{7}{17}\\\\=\dfrac{1}{2}(\dfrac{10}{15}+\dfrac{7}{17})\\\\=\dfrac{1}{2}(\dfrac{170+105}{255})\\\\=\dfrac{1}{2}\times \dfrac{275}{255}\\\\=\dfrac{275}{510}=\dfrac{55}{102}$

Hence, Probability of taking red ball from one of the bags is $\dfrac{55}{102}$