Question

A bag contains 4 red and 3 black balls .a second bag contains 2 red and 3 black balls. one bag is selected at random.if from the selected bag one ball is drawn then what is the probability that the ball drawn is red

Answer 1

If from the selected bag one ball is drawn then the probability that the ball drawn is red is 17/35.

Step-by-step explanation:

It is given that,

Bag 1 contains: 4 red and 3 black balls

Bag 2 contains: 2 red and 3 black balls

Let’s assume the following:

“E1” = event of selecting bag 1

“E2” = event of selecting bag 2

“A” = event of drawing a red ball

We can say that a red ball can be drawn in two ways:

• Selecting bag 1 and then drawing a red ball from it.

 

• Selecting bag 2 and then drawing a red ball from it.

 

Since one of the two bags is selected randomly, then

Probability of selecting bag 1, P(E1) = ½  

And,

Probability of selecting bag 2,  P(E2) = ½

Now,  

Probability of drawing a red ball if the first bag has been selected, P(A/E1) = 4/7

And,

Probability of drawing a red ball if the second bag has been selected, P(A/E2) = 2/5

Thus,  

If from the selected bag one ball is drawn then the probability that the ball drawn is red, P(red ball) or P(A), is given by,

= [P(E1)*P(A/E1)] + [P(E2)*P(A/E2)]

= [(½) * (4/7)] + [(½) * (2/5)]

= [2/7] + [1/5]

= [10+7] / [35]

= 17/35

-----------------------------------------------------------------------------------------

Also View:

A bag contains 8 red balls and 5 white balls r drawn from the bag what is the probability of getting white balls ?

https://brainly.in/question/9985598

A bag contains 6 white and 4 black balls. Two balls are drawn at random. The probability that they are of the same colour, is?

https://brainly.in/question/3668778

A bag contains 15 white and some black balls . If the probability of drawing a black ball from the bag is thrice that of drawing a white ball, find the number of black balls in the bag.

https://brainly.in/question/1141576