Final answer:
To find the probability of not drawing a diamond twice in a row from a standard deck of cards without replacement, multiply the probability of not drawing a diamond on the first draw (39/52) by the probability of not drawing a diamond on the second draw (38/51).
Step-by-step explanation:
The student is asking about the probability of drawing cards from a standard deck without replacement. Drawing cards without replacement means that each draw affects the outcome of the next draw, as the card drawn is not put back into the deck, thereby reducing the total number of cards.
To find the probability of not drawing a diamond (D) twice in a row without replacement, calculate the probability of not drawing a diamond on the first draw and multiply it by the probability of not drawing a diamond on the second draw given that the first card was not a diamond. In a standard deck of 52 cards, there are 13 diamonds. The probability of not drawing a diamond on the first draw is 39/52, because there are 39 cards that are not diamonds. After drawing one non-diamond card, there are 51 cards left in the deck, and 38 of them are not diamonds. The probability of not drawing a diamond on the second draw is therefore 38/51.
To find the combined probability, you multiply the two probabilities:
P(Not D, then not D) = (39/52) * (38/51)
Upon calculating, this gives us the probability of not drawing a diamond twice in a row without replacement.