Find the probability that they buy toothbrushes of the same colour?

Question

John and Eric share aflat, so it would be confusing If their toothbrushes were the same colour.on the first day of term They both go to the shop to buy a toothbrush.For each of James and Simon, the probabilities of buying red,blue,green,purple and white toothbrushes are 3/8,1/4,1/8,1/8,1/8 respectively The choices of John and Eric are independent.Find the probability that they buy toothbrushes of the same colour.

Comments

How will you state the fomula pls ?

Answer 1

	Red	Blue	Green	Purple	White
Red	9/64	3/32	3/64	3/64	3/64
Blue	3/32	1/16	1/32	1/32	1/32
Green	3/64	1/32	1/64	1/64	1/64
Purple	3/64	1/32	1/64	1/64	1/64
White	3/64	1/32	1/64	1/64	1/64

We simply sum the squares of the probabilities for each colour: (3/8)^2+(1/4)^2+3(1/8)^2=1/4.

The diagonal cells in the table represent the sum of the squares of the probabilities. The total of all 25 cells is 1.