A card is drawn from a well-shuffled deck of 52 playing cards. Let E denote the event that the card drawn is black and let F denote the event that the card drawn is a spade . Determine whether E and F are independent events. Follow this process: For 1 to 3 enter your answers as reduced fractions like 1/3, 1/36... as appropriate. Note: Your answers are not limited to the examples above. 1. E - event that the card drawn is black. P(E) = 2. F - event that the card drawn is a spade. P(F)= 3. P(E ∩ F)=
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.
A card is drawn from a well-shuffled deck of 52 playing cards. Let E denote the
Follow this process:
For 1 to 3 enter your answers as reduced fractions like 1/3, 1/36... as appropriate.
Note: Your answers are not limited to the examples above.
1. E - event that the card drawn is black. P(E) =
2. F - event that the card drawn is a spade. P(F)=
3. P(E ∩ F)=
Refer to "Test for the Independence of Two Events" on page 432 for the next 2 (Yes or No)answer
Page 437 #23
The probability that a battery will last 10 hr or more is .8 , and the probability that it will last 15 hr or more is .15. Given that a battery has lasted 10 hr, find the probability that it will last 15 hours or more. (Round your answer to 4 decimal places.)
Page 437 #25a
The following table gives the percent of a country's population having each of the eight possible blood types in the
| Blood Types | A+ | A− | B+ | B− | AB+ | AB− | O+ | O− |
|---|---|---|---|---|---|---|---|---|
| Percent | 35.7 | 6.3 | 8.5 | 1.5 | 3.4 | 0.6 | 37.4 | 6.6 |
Selling a car:
A - Event a potential buyer will read the add: P(A) = .3
B - Event an advertisement is read potential buyer will buy a car: P(B) = .2
Calculate the probability that a person who reads the add will buy a car.
Calculate P(A ∩ B = ?
4. Does P(E ∩ F) = P(E) ⋅P(F)? (Yes or No)
5. Your conclusion: Are E and F independent events? (Yes or No)
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