| 8. A card is drawn at random from a well-shuffled deck of playing cards. Find the probability that the card drawn is i. a card of spade or an ace. ii. a black king. iii. neither a jack nor a king iv. either a king or a queen. Hint: In a deck of cards there are 13 spades and 4 aces. Then we have to find the probability of drawing spades from deck of cards and probability of drawing aces from deck of cards, now there is a probability of getting aces of spades so remove that probability from addition of those two probabilities. Probability of drawing an ace or a spade or both from a deck of card is denoted by \[P(A\cup B)\] Complete step-by-step answer:
We know that there are 52 cards in total.
Hence, the total number of possible outcomes is 52
Probability of drawing an ace or a spade or both from a deck of card is
The total number of spades in a deck of cards is 13
The probability of drawing spades in a deck of cards is \[P(A)=\dfrac{13}{52}\]
The total number of aces cards in a deck of cards is 4
The probability of drawing aces in a deck of cards is \[P(B)=\dfrac{4}{52}\]
The total number of aces of spade is 1
\[P(A\cap B)=\dfrac{1}{52}\]
Probability of drawing an ace or a spade or both from a deck of card is
\[P(A\cup B)=P(A)+P(B)-P(A\cap B)\]
= \[\dfrac{13}{52}+\dfrac{4}{52}-\dfrac{1}{52}=\dfrac{16}{52}=\dfrac{4}{13}\]
Probability of drawing an ace or a spade or both from a deck of cards is \[\dfrac{4}{13}\]. Note: From the venn diagram we can obtain the relation that is \[P(A\cup B)=P(A)+P(B)-P(A\cap B)\]. Here \[P(A\cup B)\]represents probability of happening of events A and B or probability of happening both.By using the formula we are able to solve the problem. We know that the probability is the ratio of total number of desired outcomes to the total number of all possible outcomes.
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What is the probability of getting a card of spade?
For example, you can add up the number of spades in a complete deck (13) and divide this by the total number of cards in the deck (52) to get the probability of randomly drawing a spade: 13 in 52, or 25 percent.
How many ways can you draw a spade or an ace?
In a standard 52 card deck, there are 13 spades and 4 aces, however one of these aces is a spade, so we need to avoid counting one ace to ensure no double-counting. So, there are 13 + 3 = 16 ways to draw an ace or a spade.
What is spade and ace?
The Ace of Spades (also known as the Spadille and Death Card) is traditionally the highest and most valued card in the deck of playing cards in English-speaking countries. The actual value of the card varies from game to game.
What will be the probability of drawing either an ace card or a king of spade from deck?
The probability of drawing either an ace or a king from a pack of card in a single draw is 2/13.
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