There are 10 yellow, 6 green, 9 orange, and 5 red cards in a stack of cards turned facedown. Once a card is selected, it is NOT replaced. Determine the p(yellow card and then green card)?
30 cards in all, so 10/30 * 6/29 = ___
To determine the probability of drawing a yellow card followed by a green card, we first need to calculate the total number of cards and the total number of favorable outcomes.
Step 1: Calculate the Total Number of Cards
To find the total number of cards, add up the number of cards of each color:
Total number of cards = number of yellow cards + number of green cards + number of orange cards + number of red cards
Total number of cards = 10 + 6 + 9 + 5 = 30 cards
Step 2: Calculate the Total Number of Favorable Outcomes
To find the total number of favorable outcomes, consider that we are drawing two cards without replacement. Thus, the number of favorable outcomes is the product of the probability of drawing a yellow card and the probability of drawing a green card after a yellow has already been drawn.
Probability of drawing a yellow card:
P(Yellow) = number of yellow cards / total number of cards
P(Yellow) = 10 / 30 = 1/3
To find the probability of drawing a green card given that a yellow card has already been drawn, we need to consider the reduced sample size. Since a yellow card has been removed, the total number of remaining cards is 30 - 1 = 29.
Probability of drawing a green card after a yellow card:
P(Green after Yellow) = number of green cards / (total number of cards - 1)
P(Green after Yellow) = 6 / 29
Now, we can find the probability of drawing a yellow card followed by a green card:
P(Yellow card and then Green card) = P(Yellow) * P(Green after Yellow)
P(Yellow card and then Green card) = (1/3) * (6/29)
P(Yellow card and then Green card) ≈ 0.069
Therefore, the probability of drawing a yellow card and then a green card is approximately 0.069 or 6.9%.