Question

calculate the probability of drawing a: green card, then drawing a blue card, with no replacement. answer as a fraction in lowest terms. enter the numerator.

Explanation:

Step1: Count total and green cards

There are 10 cards in total and 5 green cards. The probability of drawing a green - card first is the number of green cards divided by the total number of cards.
$P(\text{green first})=\frac{5}{10}=\frac{1}{2}$

Step2: Count remaining cards and blue cards

After drawing a green card without replacement, there are 9 cards left. There are 2 blue cards. The probability of drawing a blue card second given that a green card was drawn first is the number of blue cards divided by the remaining number of cards.
$P(\text{blue second}|\text{green first})=\frac{2}{9}$

Step3: Use multiplication rule for dependent events

The probability of both events happening is the product of the probabilities of each event.
$P(\text{green then blue})=P(\text{green first})\times P(\text{blue second}|\text{green first})=\frac{1}{2}\times\frac{2}{9}=\frac{2}{18}=\frac{1}{9}$

Answer:

1