Question

Tabitha has a deck of cards numbered 1−10. She picks one card, puts it back in the deck and then chooses a second card. What is the probability that she picks an even number and then a 3?

Answer 1

Tabitha has a deck of cards numbered 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. There are 5 odd numbers 1, 3, 5, 7, 9 and 5 even numbers 2, 4, 6, 8, 10.

1. She picks one card from given 10 cards. The probability that she picks an even number is

$Pr_1=\dfrac{5}{10}=\dfrac{1}{2}.$

2. She puts first card back in the deck and then chooses a second card. The probability that she picks card with number 3 is

$Pr_2=\dfrac{1}{10}.$

3. Use the product rule to determine the probability that she picks an even number and then a 3:

$Pr=Pr_1\cdot Pr_2=\dfrac{1}{2}\cdot \dfrac{1}{10}=\dfrac{1}{20}=0.05.$

Answer: 0.05.

Answer 2

First compute the whole number of the possibilities :
10*9=90.
Compute the number of favorable possibilities:
There is 5 even numbers. Once we pick an even number, 
we pick 5. So the number of the favorable possibilities is 5.
Now we compute the probability like this:
$\frac{5}{90}$