Question

In: Statistics and Probability

Consider a box with 24 beads that have either black or white color. The beads cannot...

Consider a box with 24 beads that have either black or white color. The beads cannot be distinguished otherwise. Each time you can take one bead from the box. The only thing you know is the following: in order to be certain that you pick 3 white beads, you have to take 11 beads from the box

A) What is the smallest number of beads you have to take from the box in order to be sure that at least one of them is black?

B ) What is the smallest number of beads you have to take from the box in order to be sure that there are at least three beads of each color?

C) What is the smallest number of beads you have to take from the box in order to be sure that you took at least half of the white beads from the box?

Expert Solution

let k = black beads

so white beads = 24-k

to be sure to pick atleast 3 white beads you have to pick atleast (no. of black beads + 3 = k+3) beads

given : to be certain that you pick 3 white beads, you have to take 11 beads from the box

therefore :

k+3 = 11

k = 8

so, 8 black beads and 16 white beads

A.

no. of beads to pick to be certain that atleast one balck

= no. of white + 1

= 16+1

= 17

B.

smallest number of beads you have to take from the box in order to be sure that there are at least three beads of each color

= (Larger no. of beads) + 3

= (no. of white beads) + 3

= 16+3

= 19

C.

smallest number of beads you have to take from the box in order to be sure that you took at least half of the white beads from the box

= no. of black beads + (no. of white beads)/2

= 8 + 16/2

= 16

(PLEASE UPVOTE)

orchestra answered 2 years ago

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