Suppose there are two bags of small balls. In the first bag, there are 3 red bal

Question

Suppose there are two bags of small balls. In the first bag, there are 3 red balls and 4 black balls, and in the

second bag, there are 4 red balls and 5 black balls:

•

There are two events. The first event is that you randomly pick a ball from the first bag, and the result

is a red ball. The second event is that you randomly pick a ball from the second bag, and the result is

a red ball. What is the relation between these two events?

•

What is the probability that you randomly pick one ball from each bags, and both balls you pick are

black?

Explanation / Answer

The 2 events let them be represented as:

X = You randomly pick a ball from the first bag, and the result is a red ball

Y = You randomly pick a ball from the second bag, and the result is a red ball.

The 2 events are independent to each other because getting a red ball from the first bag has no effect on the probability of drawing a red ball from the second bag.

Now the thing we have to find is:

Probability that you randomly pick one ball from each bags, and both balls you pick are black. As the 2 events are independent from each other:

P( X and Y ) = P(X) P(Y)

Now let :

P(X) = probability of drawing a black ball from the first bag

= number of black balls in first bag / total number of balls in first bag.

= 4/ 7

P(Y) = probability of drawing a black ball from the second bag

= number of black balls in second bag / total number of balls in second bag.

= 5/ 9

Therefore Probability of drawing a black ball from both the bags would be:

P(X and Y ) = (4/7)(5/9) = 20/63 = 0.3175

Therefore 0.3175 is the required probability here.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.