Answer:
16/17
Explanation:
To find the probability that two cards drawn from an ordinary deck are not both not the same suit, we can calculate the complementary probability, which is the probability that they are both the same suit. Then, we subtract this complementary probability from 1 to get the desired probability.
There are four suits in a standard deck of cards: hearts, diamonds, clubs, and spades. Let's consider the possible cases where the two cards drawn are of the same suit:
1. Both cards are hearts.
2. Both cards are diamonds.
3. Both cards are clubs.
4. Both cards are spades.
In each of these cases, there are 13 cards of the same suit remaining in the deck after the first card is drawn. So, the probability of drawing two cards of the same suit is:
P(same suit) = (13/52) * (12/51) = 1/17
Now, we can find the probability that the two cards are not both not the same suit:
P(not both not the same suit) = 1 - P(same suit)
P(not both not the same suit) = 1 - 1/17
P(not both not the same suit) = 16/17
Therefore, the probability that the two cards drawn are not both not the same suit is 16/17.
Hope it helps!! :)