# probability

This topic contains 7 replies, has 3 voices, and was last updated by  shruti290 6 years, 1 month ago.

• Author
Posts
• #498

shruti290
Participant

a box contains 30 red ballls,30 white balls and 30 blue balls if 10 balls are selected at random wht is the probability tht at least one color will be missing from the selection?

Quote
• #507

rohit pandey
Participant

take three events
A={NO RED BALL}
B={NO BLUE BALL}
C={NO WHITE BALL}
SO WE NEED TO FIND P{AUBUC}=?

SO P(A)=30C10/90C10 P(B) AND P(C) WILL BE SAME
NOW P(A∩B)=60C10/90C10 P(B∩c) and p(A∩C) WIL BE SAME

NOW P(A∩B∩C)=0 {CANT HAPPEN}
SO P(AUBUC}=3*{30C10-60C10}/90C10

Quote
• #508

shruti290
Participant

but where is the case where 2 colors will be missing?
what i thought was tht first there are 90c10 ways in total now
case1-draw 10 balls from the 30 red and 30 white balls tht means 60c10
cse 2- 10 balls drawn frm 30 white and 30 blue balls tht means 60c10
case3-10 balls frm 30 red and 30 blue tht emans 60c10
now in all these 3 cases will also involve the cases where only red ,blue or white balss are drawn therefore to avoid double counting we subtract 3*30c10
3(60c10-30c10)/90c10

Quote
• #515

rohit pandey
Participant

just one correction p(a)=60c10/90c10
and p(a∩b)=30c10/90c10

so p(aubuc)=3*{60C10-30C10}/90C10

sorry had misplaced the values as i was sleepy

and p(aubuc) covers the possibility of two balls not being selected.

Quote
• #522

Keymaster

Well done Rohit

Quote
• #523

shruti290
Participant

my final answer aslo comes out to be the same. can anyone tell me what is my mistake?

Quote
• #530

Keymaster

Shruti, you have only considered the case where exactly one colour is excluded. You haven’t accounted for the case where 2 colours are excluded

Quote
• #532

shruti290
Participant

But sir what i have done is tht first when i said tht we draw 10 balls frm 30 white and 30 blue balls so this sample will automatically include the case where either only 10 white balls are drwan or10 blue balls are drwan .so this does not becomes the case of exactly one color missing

Quote

You must be logged in to reply to this topic.