Final answer:
The probability of drawing three cards that are all spades and rolling a total of 7 on two dice is 11/2550.
Step-by-step explanation:
To find the probability that three cards are all spades and a total of 7 is rolled on the dice, we need to calculate the probability of these two independent events happening simultaneously.
To start, we need to determine the probability of drawing three spades from a well-shuffled deck without replacement.
The probability of drawing a spade on the first draw is 13/52 (since there are 13 spades in a deck of 52 cards). After the first draw, there are 12 spades left in the deck, so the probability of drawing a spade on the second draw is 12/51. Similarly, on the third draw, there are 11 spades left in the deck, so the probability is 11/50.
Therefore, the probability of drawing three spades without replacement is (13/52) * (12/51) * (11/50) = 33/850.
Next, we need to calculate the probability of rolling a total of 7 on two dice.
From rolling two dice, there are 6*6=36 possible outcomes. To get a sum of 7, there are 6 possible combinations: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1). So the probability of rolling a total of 7 is 6/36 = 1/6.
Finally, we multiply the probabilities of the two independent events to find the probability of both of them happening together: (33/850) * (1/6) = 11/2550.