Question

A batch contains 38 bacteria cells. Assume that 12 of the cells are not capable of cellular replication. Six cells are selected at random, without replacement, to be checked for replication. Round your answers to four decimal places (e.g. 98.7654).

(a) What is the probability that all six cells of the selected cells are able to replicate?

(b) What is the probability that at least one of the selected cells is not capable of replication?

Answer 1

Of the 38 cells, 12 are not capable of cellular replication and remaining (38-12) = 26 are able to replicate.

a)

number of ways to select 6 cells which are replicate from 26 cells = ²⁶C₆

Where ²⁶C₆ = 26! / [ (26- 6)! * 6! ] = 230230

Total number of ways to select 6 cells from 38 cells = ³⁸C₆ = 38! / [ (38 - 6)! * 6! ] = 2760681

P(All six cells are able to replicate) = ²⁶C₆ / ³⁸C₆

= 230230 / 2760681

= 0.0834

b)

P(At least one cell not capable of replication) = 1 - P(All six cells are able to replicate)

= 1 - 0.0834

= 0.9166