Math, asked by meghnabharadwaj18, 2 months ago

An urn contains 10 white marbles, 15 blue marbles, and 20 red marbles. Five marbles are selected, one at a time, with replacement. Find the probability that at least one color will be missing from the 5 selected marbles.

Answers

Answered by amitnrw
3

Given :  An urn contains 10 white marbles, 15 blue marbles, and 20 red marbles.

Five marbles are selected, one at a time, with replacement.

To  Find : the probability that at least one color will be missing from the 10 selected marbles.​

Solution:

White W  = 10

Blue B  = 15

Red  R = 20

Total  = 45

Five marbles are selected, one at a time, with replacement.

P (W)   - 10/45  = 2/9    => P ( not white ) = 7/9

P (B) =  15/45  =   1/3   => P ( not Blue ) =   2/3

P (R)  = 20/45  = 4/9   => P ( not Red ) =   5/9

probability that at least one color will be missing from the 10 selected marbles.​  

At least white missing  =   P( no white )  =  ( 7/9)⁵

At least Blue  missing  =   P (  no  blue ) =    ( 2/3)⁵

At least Red missing   =     P ( no red)   =     ( 5/9)⁵

At least white missing  consist of white and blue missing , white and red missing .   similarly

At least Blue  missing consist of white and blue missing , blue and red missing

At least Red missing  consist of white and Red missing , blue and red missing

Missing of   white and blue , white and red ,  blue and red   is counted twice

P ( Missing of   white and blue)  = only red =  (4/9)⁵

P ( Missing of   white and red)  = only blue =  (1/3)⁵

P ( Missing of  red and blue)  = only white =   (2/9)⁵

probability that at least one color will be missing from the 10 selected marbles.​

=  ( 7/9)⁵  +  ( 2/3)⁵  +  (5/9)⁵ - (4/9)⁵ -  (1/3)⁵-  (2/9)⁵

=    ( 7/9)⁵ +  ( 6/9)⁵  +  (5/9)⁵  - (4/9)⁵-  (3/9)⁵ -  (2/9)⁵

= ( 7⁵ + 6⁵ + 5⁵  - 4⁵  - 3⁵- 2⁵)/9⁵

=0.44724

Learn  More:

There are two urns. the first urn contains 3 red and 5 white balls ...

brainly.in/question/13404745

Two balls are drawn from an urn containing 5 green, 3 blue, 7 yellow ...

brainly.in/question/7795905

An urn contains 6 yellow, 5 blue and 2 white marbles. If three ...

brainly.in/question/11611584

Answered by arunkumarv
0

Answer:

Step-by-step explanation:

Similar questions