Answer to Question #311385 in Statistics and Probability for Rush D

Question

A card is drawn from a deck, then replaced, and a second card is drawn. Find the probability of selecting

1. two pictures card
2. a black card and an ace card
3. a diamond and a king
4. a lettered card and a number card
5. a spade and a club

Answer 1

A - considered event

1) $P(A)=({\frac {12} {52}})^2={\frac 9 {169}}$

2) $P(A)=2*{\frac {26} {52}}*{\frac 4 {52}}={\frac 1 {13}}$

3) $P(A)=2*{\frac {13} {52}}*{\frac 4 {52}}={\frac 1 {26}}$

4) $P(A)=2*{\frac {16} {52}}*{\frac {36} {52}}={\frac {72} {169}}$

5) $P(A)=2*{\frac {13} {52}}*{\frac {13} {52}}={\frac 1 8}$

In question 2-5 i assumed that order doesn't matter. If order does matter(for example, for question two first card is black and second card is ace), you should divide results by 2