S1 Question-discrete random variable

satisverborum2003

When a certain type of cell is subjected to radiation, the cell may die, survive as a single cell, or divide into two cells with probabilities 1/2, 1/3, 1/6 respectively.

Two cells are independently subjected to radiation. The random variable X represents the total number of cells in existence after this experiment.

a, Show that P(X=2) = 5/18

I'll be grateful if someone can explain this to me because I'm confused here.

Reply 1

Kolya

You can solve this question by using, albeit slightly more complicated, probability tree diagrams. Have you tried this method? It is important to be careful when interpreting the trees, so that you only count the branches that gives 2 cells left at the end.

Reply 2

insparato

1/2 - Die
1/3, - Survive one cell
1/6 - Survive two cells

Two cells are subjected

So the if its X = 2 , that means there are two cells left. So it can be

One cell Dies
One cell divides into two

Survive one cell
Surive one cell

Probability of one cell dying and one cell dividing into two is 2(1/2 x 1/6 )

Probablity of both cells surviving but stay as one cell is 1/3 x 1/3

So P(X=2) = 1/6 + 1/9 = 3/18 + 2/18 = 5/18