Question

I have three bags that each contain $100$ marbles- Bag $1$ has $75$ red and $25$ blue marbles, Bag $2$ has $60$ red and $40$ blue marbles, Bag $3$ has $45$ red and $55$ blue marbles. I choose one of the bags at random and then pick a marble from the chosen bag, also at random. What is the probability that the chosen marble is red?

• A. $0.60$
• B. $0.40$
• C. $0.50$
• D. None of these

Answer 1

The correct option is A $0.60$

Given that bag 1 contains $75$ red and $25$ blue marbles

Given that bag 2 contains $60$ red and $40$ blue marbles

Given that bag 3 contains $45$ red abd $55$ blue marbles

Now the probability of choosing red ball from bag 1 is $\frac{1}{3}\times \frac{75}{100}$

Now the probability of choosing red ball from bag 2 is $\frac{1}{3}\times \frac{60}{100}$

Now the probability of choosing red ball from bag 3 is $\frac{1}{3}\times \frac{45}{100}$

Now the probability of choosing red ball is $\frac{1}{3}\left(\frac{75+60+45}{100}\right)=0.6$

Hence, option $A$ is correct.