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 Basics of Probability

Probability is a measure of the likelihood of an event occurring. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In a standard deck of 52 cards, there are 4 suits (hearts, diamonds, clubs, spades), each with 13 cards.

Step 2: Calculate Probability of Drawing a Diamond

There are 13 diamond cards in a standard deck of 52 cards. So, the number of favorable outcomes is 13, and the total number of possible outcomes is 52. We then simplify the fraction.

Step 3: Calculate Probability of Not Drawing an Ace

There are 4 aces in a deck of 52 cards. The probability of drawing an ace is $4/52$. The probability of an event not happening is 1 minus the probability of the event happening. So, we subtract the probability of drawing an ace from 1.

Step 4: Calculate Probability of Drawing a Black Card

Black cards include clubs and spades. There are 13 clubs and 13 spades, making a total of $13 + 13 = 26$ black cards. The probability is then 26 divided by 52.

Step 5: Calculate Probability of Not Drawing a Diamond

Using the complement rule again, the probability of not drawing a diamond is 1 minus the probability of drawing a diamond. We already found that $P(\text{diamond}) = 1/4$.

Step 6: Calculate Probability of Not Drawing a Black Card

Similar to the previous steps, the probability of not drawing a black card is 1 minus the probability of drawing a black card. We previously calculated $P(\text{black card}) = 1/2$. Alternatively, red cards are not black cards, and there are 26 red cards (13 hearts + 13 diamonds).

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