1 [Four flips] If you flip a coin four times, what is the chance it will land he
ID: 3070455 • Letter: 1
Question
1 [Four flips] If you flip a coin four times, what is the chance it will land heads at least once, but not every time?
2 [Queen in five] If a five-card hand is drawn from a well-shuffled deck of cards, what is the chance at least one of the cards is a queen?
3 [Draw a spade] Draw one card with replacement from a well-shuffled standard poker deck until you draw a spade. Find the probability of each of the following:
a. You draw only once.
b. You draw at least once.
c. You draw at least twice.
d. You draw at least three times, but no more than five times
4 [Roulette: bet on black] A roulette wheel has 38 slots. These are colored as follows: 18 red, 18 black, and 2 green. A bet on black (or red) pays even money. Suppose you risk $1 on black for 20 rounds. Complete the sentence: your net gain is likely to be around ___, give or take ____ or so. (Fill in the blanks with the expected value and standard error.)
5 [Flip until heads] If a coin will be flipped until it lands heads, what is the chance it will be flipped more than ten times?
6. [Two Colors Marbles] Suppose a box has 4 red marbles and 6 blue marbles. a. If we draw two marbles without replacement, what is the chance of getting this sequence: blue, then red? b. If we draw two marbles without replacement, what is the chance of getting one of each color (in any order)?
7. [Three Colors Marbles] Suppose a box has 5 red marbles, 6 green marbles, and 7 blue marbles. a. If we draw three marbles without replacement, what is the chance of getting this sequence: blue, then green, then red? b. If we draw three marbles without replacement, what is the chance of getting one of each color (in any order)?
8. [Positive test] A patient is tested for a virus that is believed to be present in 5% of the population. If the test result is positive, compute the chance the patient actually has the virus… a. If the false-positive rate is 4% and the false-negative rate is 1% b. If the false-positive rate is 2% and the false-negative rate is 0.3% c. If the false-positive rate is 0.1% and the test never gives a false negative. d. If the test never gives a false-positive or a false-negative.
9. [Two cards] A standard deck of 52 poker cards is well shuffled, and the top two cards are drawn and placed face-down on a table. What is the chance that one of them is a jack and the other is a 10?
Explanation / Answer
#1.
If four coins are flipped, there are 2^4 = 16 possible outcomes.
consider an outcome with no heads and all heads there are 2 such outcomes.
Required probability = 1- 2/16 = 7/8
#2.
5 cards from 52 cards can be drawn in 52C5 ways.
Consider an event such that no card is queen, i.e. 5 cards are selected from 48 cards. this can be done in 48C5
Required probability = 1 - 48C5/52C5
= 0.3412
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.