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.
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Step-by-Step Solution
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(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(black card)=1/2. Alternatively, red cards are not black cards, and there are 26 red cards (13 hearts + 13 diamonds).