A bag contains 3 red and 7 black balls

Asked by admin @ 17/08/2021 in Math viewed by 291 People

A bag contains 3 red and 7 black balls. Two balls are selected at random with replacement. If second selected is given to be red, what is the probability that first selected is also red

Answered by admin @ 17/08/2021

Answer:

2/9

Step-by-step explanation:

Let:

R1 be the event that the first ball is red
B1 be the event that the first ball is black
R2 be the event that the second ball is red

We are asked for the conditional probability P( R1 | R2 ).

P( R1 | R2 ) = P( R1 ∩ R2 ) / P( R2 )

= P( R2 | R1 ) P( R1 ) / P( R2 ) ... (*)

Deal with the numerator and denominator here separately.

Numerator

P( R1 ) = ( # red balls at start ) / ( # balls at start )

= 3 / 10

P( R2 | R1 ) = ( # red balls after selecting one ) / ( # balls after selecting one )

= 2 / 9

So the numerator is:

3/10 × 2/9 = 1 / 15

Denominator

By the Law of Total Probability,

P( R2 ) = P( R2 | R1 ) P ( R1 ) + P( R2 | B1 ) P( B1 )

The first term here is just the numerator that we worked out above.

For the second term:

P( B1 ) = ( # balck balls at start ) / ( # balls at start )

= 7 / 10

P( R2 | B1 ) = ( # red balls after selecting black ) / ( # balls after selecting one )

= 3 / 9 = 1 / 3

Thus...

P ( R2 ) = 1/15 + 7/10 × 1/3

= 2/30 + 7/30

= 9 / 30

= 3 / 10

Putting it together

Going back to equation (*), we now have

P( R1 | R2 ) = P( R2 | R1 ) P( R1 ) / P( R2 )

= ( 1/15 ) / ( 3/10 )

= 10 / ( 15 × 3 )

= 10 / 45

= 2 / 9

A bag contains 4 red and 3 black balls

Asked by admin @ 17/08/2021 in Math viewed by 300 persons

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 …

A bag contains white black and red balls only

Asked by admin @ 13/08/2021 in Math viewed by 299 persons

A bag contains white, black and red balls only. A ball is drawn at random from the bag. If the probability of getting a white ball is 3/10 and that …

A bag contains 4 red and 6 black balls

Asked by admin @ 13/08/2021 in Math viewed by 309 persons

a bag contains 4 red and 6 black balls .a ball is drawn at random from the bag its colour is observed and this ball along with two additional balls …

A bag contains 5 black and 6 red balls

Asked by admin @ 12/08/2021 in Math viewed by 345 persons

Question 8 A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected. Class X1 - …

A bag contains 5 white and 7 black balls

Asked by admin @ 23/08/2021 in Math viewed by 329 persons

33. A bag contains 5 white and 7 black balls. Another bag contains 7 white and 8 black balls. A ball is taken at random from the first bag and …

A bag contains 5 white balls 7 red balls

Asked by admin @ 20/08/2021 in Math viewed by 307 persons

A bag contains 5 white balls, 7 red balls, 4 black balls and 2 blue balls. One ball is drawn at random from the bag. Find the probability that the …

A bag contains 5 red and 3 blue balls

Asked by admin @ 23/08/2021 in Math viewed by 403 persons

A bag contains 5 red and 3 blue balls. If 3 balls are drawn at random without replacement then find the probability of getting exactly one red ball.

An urn contains 5 red and 5 black balls

Asked by admin @ 13/08/2021 in Math viewed by 348 persons

An urn contains 5 red and 5 black balls. A ball is drawn at random, its colour is noted and is returned to the urn. Moreover, 2 additional balls of …

A bag contains 6 black and 8 white balls

Asked by admin @ 11/08/2021 in Math viewed by 377 persons

A bag contains 6 black and 8 white balls one ball is drawn at random what is the probability that the ball drawn is white

An urn contains 5 red and 2 black balls

Asked by admin @ 20/08/2021 in Math viewed by 255 persons

an urn contain 5 red and 2 black balls , two balls are randomly drawn without replacement . let x represent number of black ball draw .what are the possible …

A bag contains 8 red and 5 white balls

Asked by admin @ 17/08/2021 in Math viewed by 352 persons

A bag contains 5 white and 8 red balls. two drawing of 3 balls are made such that (a) balls are replaced before the second trial (b) the balls are …

A bag contains 4 red balls and 5 black balls

Asked by admin @ 02/08/2021 in Math viewed by 331 persons

A bag contains 4 red and 5 black balls. Another bag contains 5 red, 3 black balls. If one ball is drawn at random from each bag. Then the probability …

An urn contains 3 white and 6 red balls

Asked by admin @ 23/08/2021 in Physics viewed by 332 persons

An urn contains 3 white and 6 red balls. Four balls are drawn one by one with replacement from the urn. Find the probability distribution of the number of red …

A bag contains 6 white and 4 black balls

Asked by admin @ 12/08/2021 in Math viewed by 288 persons

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

An urn contains 7 white balls and 3 red balls

Asked by admin @ 06/08/2021 in Math viewed by 357 persons

an urn contains 7 white balls and 3 red balls. two balls are drawn together at random from this urn. compute probability that neither of them is white. hence compute …