Question

A box holds 8 red and 4 blue beads. Three beads are taken from the box and not replaced. Determine: The probability that all three beads taken are red The probability that there are at least two blue beads from the three that were taken

Answer 1

Answer:
`(14)/(55), (13)/(55)`

Explanation:

Given

There are 8 red and 4 blue beads

Three beads were taken from the box

(i)No of ways of choosing three red beads out of 12 beads is
`^8C_3`

Total no of ways
`^(12)C_3`

Probability is

`P=(^8C_3)/(^(12)C_3)=(8* 7* 6)/(12* 11* 10)=(2* 7)/(11* 5)\\P=(14)/(55)`

(ii)atleast two beads refers to minimum two beads

There can be two possibilities (2B,1 R), (3B, 0R)

`\Rightarrow P=(^4C_2* ^8C_1)/(^(12)C_3)+(^4C_3)/(^(12)C_3)\\\\\Rightarrow P=(6* 8)/(220)+(4)/(220)=(52)/(220)\\\\\Rightarrow P=(13)/(55)`