1. A stationary box contains 3 fountain pens, 5 pencils and 9 ball pens. If four items are drawn at random one by one without replacement, find the probability of getting all ball pens?
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.
1. A stationary box contains 3 fountain pens, 5 pencils and 9 ball pens. If four items are drawn at random one by one without replacement, find the probability of getting all ball pens?
2. Ali shows symptoms of Malaria and advised by the doctor to get tested for confirmation. The prescribed test method comes positive 85% of the time the patient actually has Malaria. The test method gives false positive 10% of the time, i.e when the patient does not have Malaria. If 1.5% of the population is affected by Malaria, what is the probability that Ali has been infected by Malaria provided he tested positive?
3. A jar contains 7 marbles out of which 1 is red, 4 are yellow and 2 are blue. Two marbles are drawn at random with replacement, what is the probability of getting a blue or a red marble at the end of second trial?
4. In an intelligence test, a person is shown some colored cards one by one fastly, out of which 65% of were blue and 35% were green. The probability of surity given third card is green is 90%. Use this information to deduce how likely is it that the third card actually was green if the provided surity is used?
5. 19 apples in a carton have numbers written from 1 to 19. Three apples are taken out of the carton without replacement. What is the probability that all the apples have even numbers on them?
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