In such a deck of cards there are four suits of 13 cards each. The four suits are: hearts, diamonds, clubs, and spades. The 26 cards included in hearts and diamonds are red. The 26 cards included in clubs and spades are black. The 13 cards in each suit are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This means there are four Aces, four Kings, four Queens, four 10s, etc., down to four 2s in each deck.You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second.(a) Are the outcomes on the two cards independent? Why?No. The events cannot occur together.No. The probability of drawing a specific second card depends on the identity of the first card. Yes. The probability of drawing a specific second card is the same regardless of the identity of the first drawn card.Yes. The events can occur together.(b) Find P(ace on 1st card and nine on 2nd). (Enter your answer as a fraction.)(c) Find P(nine on 1st card and ace on 2nd). (Enter your answer as a fraction.)(d) Find the probability of drawing an ace and a nine in either order. (Enter your answer as a fraction.)
The probability of drawing a diamond-faced card from a pack of 52 playing cards is easy to determine. Since there are 13 diamond-faced cards in the deck, the probability becomes 13/52 = 1/4 = 0.25.
The probability of drawing an ace from a pack of 52 playing cards is also easy to determine. There are 4 aces in the deck of 52 cards; thus, the probability becomes 4/52 = 1/13 = 0.076923. This represents a much lower probability than drawing a card in a specific suit, illustrated in the preceding example.
A branch of mathematics that deals with the happening of a random event is termed probability. It is used in Maths to predict how likely events are to happen. The probability of any event can only be between 0 and 1 and it can also be written in the form of a percentage.
The probability of event A is generally written as P(A). Here, P represents the possibility and A represents the event. It states how likely an event is about to happen. The probability of an event can exist only between 0 and 1 where 0 indicates that event is not going to happen i.e. Impossibility and 1 indicates that it is going to happen for sure i.e. Certainty.
If not sure about the outcome of an event, take help of the probabilities of certain outcomes, how likely they occur. For a proper understanding of probability, take an example of tossing a coin, there will be two possible outcomes – heads or tails.
Formula of Probability
There are different terms used in the probability that is not commonly used normally, terms like experiments, sample space, a favorable outcome, trial, random experiment, etc. Let’s take a look at their definitions in detail,
Some Probability Formulae
Question 1: What is the probability of getting a queen or a red card?
Question 2: What is the probability of drawing a black card from a well-shuffled deck of 52 cards?
Question 3: What is the probability of getting a black queen or a diamond?
Question 4: Find the probability of getting a number less than 5 in a single dice throw.
Question 5: What are the odds of flipping 7 heads in a row?
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