There are ten yellow 6 green 9 orange and 5 red cards in a stack of cards turned faced down once a card is selected it is not replaced what is the probability they will get two yellow cards
yellow cards: 10 of 30 total
so,
P(y,y) = 10/30 * 9/29 = 3/29
To find the probability of selecting two yellow cards from the stack without replacement, we need to know the total number of cards and the number of possible outcomes that include two yellow cards.
First, let's calculate the total number of cards in the stack:
Total cards = Number of yellow cards + Number of green cards + Number of orange cards + Number of red cards
Total cards = 10 yellow + 6 green + 9 orange + 5 red
Total cards = 30 cards
Next, we need to find the number of ways to select two yellow cards from the stack. We can use the combination formula:
Number of ways to select 2 yellow cards = C(n, r) = n! / (r! * (n-r)!)
where n is the total number of yellow cards and r is the number of cards we want to select (in this case, 2).
Number of ways to select 2 yellow cards = C(10, 2) = 10! / (2! * (10-2)!)
Number of ways to select 2 yellow cards = 10! / (2! * 8!)
Number of ways to select 2 yellow cards = (10 * 9 * 8!) / (2 * 1 * 8!)
Number of ways to select 2 yellow cards = (10 * 9) / (2 * 1)
Number of ways to select 2 yellow cards = 45
Lastly, we can calculate the probability by dividing the number of favorable outcomes (selecting two yellow cards) by the total number of possible outcomes (selecting any two cards from the stack):
Probability of getting two yellow cards = Number of ways to select 2 yellow cards / Total number of cards
Probability of getting two yellow cards = 45 / 30
Probability of getting two yellow cards = 3/2
Probability of getting two yellow cards = 0.5 or 50%
Therefore, the probability of selecting two yellow cards from the stack is 0.5 or 50%.