LONG MATH QUESTION! please help?

Question

The Letters G,E,O,M,E,T,R,Y are written on a set of cards. You mix the cards thoroughly. without looking, you draw one letter, replace it, then draw another card. Find Each Probability




P(E,T) ????????????




P(M,Y) ????????????????????

Answer 1

P (E,T) = 2/8 X 1/8 = 1/32
P (M,Y) = 1/8 X 1/8 = 1/64

Answer 2

If P(E,T) means first getting an E and then a T, the probability is 2/8 x 1/8 = 2/64=1/32. There are 8 letters, 2 E's and 1 T. If it means getting an E and a T in either order, the result is twice that. Similarly P(M,Y) = 1/8 x 1/8 = 1/64 or 2/64.

Answer 3

This is "a priori" prob, as opposed to Bayesian.

So the first problem involved a 1/4 probability of drawing an E followed by a 1/8 probability of drawing an T, or 1/32.

In the second problem, both drawings have a 1/8 probability of success, the the probabilty is 1/64

Answer 4

If you replace the cards the draws are independent of each other and not conditional. Think of it almost like rolling two 8-sided dice with letters instead of pips.

So if P(E) = 2/8 (two Es out of 8) and P(T)=1/8 and
P(M) = 1/8 and P(Y) = 1/8, then the two probabilities are:

2/64 and 1/64.

Answer 5

the probability will be the same since you replace each time. the probability is a 1 in 8 chance for all of them. had the cards not been replaced it would be different.

Answer 6

P(E,T) = (2/7)(1/7) = 2/49 (there are 2 letters E out of 7, but only one letter T).
P(M,Y) = (1/7)^2 = 1/49 (there's one letter M and one letter Y)
Regards
Tonio