One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, calculate the probability that the card will be (i) a diamond (ii) not an ace (iii) a black card (i.e., a club or, a spade) (iv) not a diamond (v) not a black card.

Step 1: Understand the Deck and Basic Probability

A standard deck of playing cards has 52 cards. These cards are divided into four suits: hearts, diamonds, clubs, and spades. Each suit has 13 cards. Hearts and diamonds are red, while clubs and spades are black. The probability of an event is calculated as the number of favorable outcomes divided by the total number of possible outcomes.

Step 2: Calculate Probability of Drawing a Diamond

There are 13 diamond cards in a deck of 52 cards. To find the probability of drawing a diamond, we divide the number of diamond cards by the total number of cards.

Step 3: Calculate Probability of Not Drawing an Ace

There are 4 aces in a deck of 52 cards. Therefore, the number of cards that are not aces is $52 - 4 = 48$. The probability of not drawing an ace is the number of non-ace cards divided by the total number of cards.

Step 4: Calculate Probability of Drawing a Black Card

Black cards consist of clubs and spades. There are 13 clubs and 13 spades, making a total of $13 + 13 = 26$ black cards. The probability of drawing a black card is the number of black cards divided by the total number of cards.

Step 5: Calculate Probability of Not Drawing a Diamond

The probability of an event not happening is 1 minus the probability of the event happening. Since the probability of drawing a diamond is $1/4$, the probability of not drawing a diamond is $1 - 1/4 = 3/4$. Alternatively, there are $52 - 13 = 39$ non-diamond cards, so the probability is $39/52 = 3/4$.

Step 6: Calculate Probability of Not Drawing a Black Card

Similar to the previous step, the probability of not drawing a black card is 1 minus the probability of drawing a black card. Since the probability of drawing a black card is $1/2$, the probability of not drawing a black card is $1 - 1/2 = 1/2$. Alternatively, red cards are not black cards, and there are 26 red cards (13 hearts + 13 diamonds), so the probability is $26/52 = 1/2$.

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