Given a standard deck of playing cards (which you may google if you wish to see an image), the deck is shuffled and a single card is drawn at random from the deck. Determine: Which of the following pairs of events is independent? a. Pulling a Jack and pulling a face card b. Pulling a spade and pulling a black card c. Pulling a heart and pulling a Queen d. Pulling a face card and pulling an Ace e. Pulling a King and pulling a number card
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.
Given a standard deck of playing cards (which you may google if you wish to see an image), the deck is shuffled and a
single card is drawn at random from the deck. Determine:
Which of the following pairs of
a. Pulling a Jack and pulling a face card
b. Pulling a spade and pulling a black card
c. Pulling a heart and pulling a Queen
d. Pulling a face card and pulling an Ace
e. Pulling a King and pulling a number card
A deck of cards consists of 52 cards which are further divided into 4 groups with 13 cards in each group- clubs, diamonds, hearts, spades.
Each set of 13 cards consists of an ace, jack, king, queen, and the remaining cards numbered from 2 to 10.
Now, for a pair of events to be independent,
a. Let, J=pulling a Jack
F=pulling a face card
So, the events are not independent as the given condition is not satisfied.
b. Let, S=pulling a spade
B=pulling a black card
So, the events are not independent as the given condition is not satisfied.
c. Let, H=pulling a heart
Q=pulling a Queen
Here, the given condition is satisfied. Hence the events are independent.
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