Final answer:
This question is about calculating probabilities in a Mathematics context, focusing on drawing cards from a shuffled set in various scenarios and whether the draws are with or without replacement.
Step-by-step explanation:
To calculate the probability of specific outcomes when drawing two cards without replacement from a deck containing 5 green cards and 5 yellow cards, let's consider different scenarios:
Probability of drawing two green cards:
There are 5 green cards in the deck and 10 total cards. When drawing the first card, the probability of selecting a green card is 5/10. After selecting one green card, there are 4 green cards left out of 9 remaining cards. Therefore, the probability of drawing another green card on the second draw, given that the first was green, is 4/9.
To find the combined probability of both events occurring (drawing two green cards), you multiply the individual probabilities:
Probability = (5/10) * (4/9) = 20/90 = 2/9
Probability of drawing two yellow cards:
Similarly, there are 5 yellow cards in the deck. The probability of drawing a yellow card on the first draw is 5/10. After drawing one yellow card, there will be 4 yellow cards left out of 9 remaining cards. Therefore, the probability of drawing another yellow card, given that the first was yellow, is 4/9.
Combining both probabilities:
Probability = (5/10) * (4/9) = 20/90 = 2/9
Probability of drawing one green card and one yellow card:
This scenario involves two different outcomes: a green card followed by a yellow card, or a yellow card followed by a green card. We calculate both probabilities and add them together.
Probability of green then yellow = (5/10) * (5/9) = 25/90
Probability of yellow then green = (5/10) * (5/9) = 25/90
Combined probability = Probability of green then yellow + Probability of yellow then green
= 25/90 + 25/90
= 50/90
= 5/9
Therefore, the probabilities for the specific outcomes are:
Drawing two green cards: 2/9
Drawing two yellow cards: 2/9
Drawing one green card and one yellow card: 5/9