In a standard deck of 52 playing cards, there are 2 black kings: the king of spades and the king of clubs.

1. Total number of possible outcomes (total number of cards): There are 52 cards in a standard deck.

2. Total number of favorable outcomes (black kings): There are 2 black kings in the deck.
   

To find the probability that two different friends have different birthdays, we can consider the total number of possible combinations of birthdays and the number of combinations where the birthdays are different.

In a non-leap year, there are 365 days. Therefore, the probability that two friends have different birthdays is the complement of the probability that they have the same birthday.

1. Total number of possible combinations of birthdays: Each friend can have their birthday on any of the 365 days of the year. So, the total number of possible combinations of birthdays for two friends is 365×365365×365.

2. Number of combinations where the birthdays are different: If one friend has their birthday on a specific day, the other friend can have their birthday on any of the other 364 days of the year. So, the number of combinations where the birthdays are different is 365×364365×364.

Now, let's calculate the probability that two different friends have different birthdays:

Probability=Number of combinations where the birthdays are differentTotal number of possible combinations of birthdays

To find the probability of not drawing a white marble, we need to consider the total number of marbles in the box and the number of marbles that are not white.

Given:

• 3 blue marbles
• 2 white marbles
• 4 red marbles
  

To find the probability of getting a number less than 3 when a die is thrown once, we need to determine the total number of favorable outcomes (rolling a number less than 3) and divide it by the total number of possible outcomes (rolling any number on the die).

Given:

• The die has 6 faces numbered 1 through 6.

1. Total number of possible outcomes: There are 6 possible outcomes when rolling a die.

2. Number of favorable outcomes (rolling a number less than 3): There are 2 favorable outcomes: rolling a 1 or rolling a 2.

Now, let's calculate the probability of getting a number less than 3:

When a standard six-sided die is thrown once, the possible outcomes are the numbers 1, 2, 3, 4, 5, and 6.

To find the probability of getting a number greater than 5, we need to determine the number of favorable outcomes (rolling a number greater than 5) and divide it by the total number of possible outcomes (rolling any number on the die).

Given:

• Total number of possible outcomes: 6 (since there are 6 faces on the die).

1. Number of favorable outcomes (rolling a number greater than 5): There is only 1 favorable outcome: rolling a 6.

Now, let's calculate the probability: