A biased coin is flipped 20 times in a row. The coin has a probability 0.75 of showing Heads.
a. What’s the probability that you get exactly 8 Heads?
b. What’s the probability that you get exactly 8 Heads, given that the first 2 flips show Heads?
c. What’s the probability that you never see the same result consecutively( never see 2H or 2T in a row)
In: Statistics and Probability
A student club has 65 members; of these members, 28 are male and 22 are freshmen. Of the males, 10 are also freshmen.
What is the probability that a randomly selected student in the club is a freshman?
What is the probability that a randomly selected student in the club is a male or a freshman?
What is the probability that a randomly selected student in the club is male given that the student is a freshman?
What is the probability that a randomly selected student in the club is male and a freshman?
In: Statistics and Probability
Amazen has a collection of books for sale. They are either paperbacks or hardcovers and either fiction or nonfiction. Forty percent of the books are fiction and 65% are paperbacks, Also, 25% of the fiction books are hardcover. Now, a book is selected at random. a. What is the probability that it is a paperback? b. What is the probability that it is a paperback, given that it is a fiction? c. What is the probability it is a nonfiction, given that it is hardcover? d. What is the probability it is either nonfiction or paperback?
In: Statistics and Probability
Amazen has a collection of books for sale. They are either paperbacks or hardcovers and either fiction or nonfiction. Forty percent of the books are fiction and 65% are paperbacks, Also, 25% of the fiction books are hardcover. Now, a book is selected at random. a. What is the probability that it is a paperback? b. What is the probability that it is a paperback, given that it is a fiction? c. What is the probability it is a nonfiction, given that it is hardcover? d. What is the probability it is either nonfiction or paperback?
In: Statistics and Probability
A box contains 5 red marbles, 9 blue marbles, and 11 green marbles. We draw two marbles randomly without replacement. Which ones are correct?
In: Statistics and Probability
Next, determine the probability of getting an obscure ratio or worse. That is: (a)What is the probability of having 33% boys or less? (in 1000 births, 330 would be male) (b)What is the probability of having 41% boys or less? (in 1000 births,410 would be male) (c)What is the probability of having 1200 boys for every 1000 girls or 54.5% boys? (in 1000 births, 545 would be male)
In: Statistics and Probability
An ambulance station has one vehicle and two demand locations, A and B. the probability that the ambulance can travel to a location in under 8 minutes is .58 for location A and .42 for location B. the probability that the ambulance is busy at any point in time is .30.
a. Find the probability that EMS can meet demand for an ambulance at Location A.
b. Find the probability that EMS can meet demand for an ambulance at location B.
In: Statistics and Probability
There six houses on a block. Two of these houses have pools. Three houses on this block are selected at random.
A. Find the probability that exactly 0 of the selected houses have a pool.
B. Find the probability that exactly 2 of the selected houses have a pool.
C. Find the probability that all of the selected houses have a pool.
D. Find the probability that at least 1 of the selected houses has a pool.
In: Statistics and Probability
Suppose that the chance of rain tomorrow depends on previous weather conditions only through whether or not it is raining today and not on past weather conditions. Suppose also that if it rains today, then it will rain tomorrow with probability 0.6, and if it does not rain today, then it will rain tomorrow with probability 0.3, then
a. Calculate the probability that it will rain four days from today given that it is raining today.
b. What is the limiting probability of rain.
In: Statistics and Probability
A Shopping Mall sells trays of eggs of which some are returned because they are defective and it has been observed that 15% of the trays are defectives. The defective and no defective trays where observed on a random manner. If 8 trays are randomly collected, Find :-
a) The probability that exactly 2 of them are defective
b) The probability that at least 3 are defective
c) The probability that at most 2 are defective
d) The probability that no tray is defective
In: Statistics and Probability