The following question involves a standard deck of 52 playing cards. 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? O Yes. The events can occur together. O Yes. The probability of drawing a specific second card is the same regardless of the identity of the first drawn card. O No. The probability of drawing a specific second card depends on the identity of the first card. O No. The events cannot occur together. (b) Find P(ace on 1st card and king on 2nd). (Enter your answer as a fraction.) (c) Find P(king on 1st card and ace on 2nd). (Enter your answer as a fraction.) (d) Find the probability of drawing an ace and a king in either order. (Enter your answer as a fraction.)
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
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?
(b)
Find P(ace on 1st card and king on 2nd). (Enter your answer as a fraction.)
(c)
Find P(king on 1st card and ace on 2nd). (Enter your answer as a fraction.)
(d)
Find the
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