According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. (Round your answers to 4 decimal places where possible) a. Compute the probability that a randomly selected peanut M&M is not green. b. Compute the probability that a randomly selected peanut M&M is green or red. c. Compute the probability that two randomly selected peanut M&M’s are both brown. d. If you randomly select six peanut M&M’s, compute that probability that none of them are orange. e. If you randomly select six peanut M&M’s, compute that probability that at least one of them is orange.
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.
According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. (Round your answers to 4 decimal places where possible)
a. Compute the
b. Compute the probability that a randomly selected peanut M&M is green or red.
c. Compute the probability that two randomly selected peanut M&M’s are both brown.
d. If you randomly select six peanut M&M’s, compute that probability that none of them are orange.
e. If you randomly select six peanut M&M’s, compute that probability that at least one of them is orange.
2. You toss a fair coin 4 times. What is the probability that (round to 4 decimal places)
a) you get all Tails?
b) you get at least one Head?
3. With one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is accepted if every item in the sample is okay. The ABC Electronics Company has just manufactured 1350 write-rewrite CDs, and 90 are defective. If 3 of these CDs are randomly selected for testing, what is the probability that the entire batch will be accepted?
4. When doing blood testing for a viral infection, the procedure can be made more efficient and less expensive by combining partial samples of different blood specimens. If samples from three people are combined and the mixture tests negative, we know that all three individual samples are negative. Find the probability of a positive result for three samples combined into one mixture, assuming the probability of an individual blood sample testing positive for the virus is 0.08.
5. Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manager assures you that 17 of the 65 boxes on the shelf have the secret decoder ring. The other 48 boxes on the shelf have a different gift inside. If you randomly select two boxes of cereal from the shelf to purchase, what is the probability that BOTH of them have the secret decoder ring?
Trending now
This is a popular solution!
Step by step
Solved in 7 steps
