Individual A has a circle of five close friends (B, C, D,E, and F). A has heard a certain rumor from outside thecircle and has invited the five friends to a party to circulatethe rumor. To begin, A selects one of the five atrandom and tells the rumor to the chosen individual.That individual then selects at random one of the fourremaining individuals and repeats the rumor. Continuing,a new individual is selected from those not already havingheard the rumor by the individual who has just heardit, until everyone has been told.a. What is the probability that the rumor is repeated inthe order B, C, D, E, and F?b. What is the probability that F is the third person atthe party to be told the rumor?c. What is the probability that F is the last person tohear the rumor?d. If at each stage the person who currently “has” therumor does not know who has already heard it andselects the next recipient at random from all fivepossible individuals, what is the probability that Fhas still not heard the rumor after it has been told tentimes at the party?
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.
Individual A has a circle of five close friends (B, C, D,
E, and F). A has heard a certain rumor from outside the
circle and has invited the five friends to a party to circulate
the rumor. To begin, A selects one of the five at
random and tells the rumor to the chosen individual.
That individual then selects at random one of the four
remaining individuals and repeats the rumor. Continuing,
a new individual is selected from those not already having
heard the rumor by the individual who has just heard
it, until everyone has been told.
a. What is the
the order B, C, D, E, and F?
b. What is the probability that F is the third person at
the party to be told the rumor?
c. What is the probability that F is the last person to
hear the rumor?
d. If at each stage the person who currently “has” the
rumor does not know who has already heard it and
selects the next recipient at random from all five
possible individuals, what is the probability that F
has still not heard the rumor after it has been told ten
times at the party?
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