Respuesta :
Answer:
Part (A) The probability that all six cells are able to replicate is 0.069.
Part (B) The probability that at least one of the selected cells is not capable of replication is 0.931.
Step-by-step explanation:
Consider the provided information.
A batch contains 36 bacteria cells. Assume that 12 of the cells are not capable of cellular replication.
That means 36-12=24 are capable of cellular replication.
Part a) What is the probability that all six cells of the selected cells are able to replicate?
Let X = all six cells are able to replicate
[tex]P(X)=\frac{24}{36}\times\frac{23}{35}\times\frac{22}{34}\times\frac{21}{33}\times\frac{20}{32}\times\frac{19}{31}\\P(X)\approx0.069[/tex]
Hence, the probability that all six cells are able to replicate is 0.069.
Part b)What is the probability that at least one of the selected cells is not capable of replication?
For this subtract 1-P(X)
[tex]P(\text{At least one cell is not replication})=1-(\frac{24}{36}\times\frac{23}{35}\times\frac{22}{34}\times\frac{21}{33}\times\frac{20}{32}\times\frac{19}{31})\\\\P(X)\approx1-0.069\\\\P(X)=0.931[/tex]
Hence, the probability that at least one of the selected cells is not capable of replication is 0.931.
