Sample Space
What is the set of numbers between 1 and 20 that are prime?
{2, 3, 5, 7, 11, 13, 17, 19}
In a group of 92 students, 35 have brown eyes and 21 have hazel eyes. Find the probability that a student picked from this group either has brown or hazel eyes.
35/92 + 21/92 = 56/92
John rolled a die twice what is the probability of rolling an odd number on the first roll and a 2 on the second roll?
3/6 x 1/6 = 4/36
You have two events A and B such that P(A|B) = 0.8 and P(A) = 0.8. Based on this information, what can you conclude?
Event A is not dependent on Event B.
A bag contains six blue balls and five red balls. A sample of four balls is selected at random from the bag. What is the probability that the sample contains two blue balls and two red balls? Round to nearest hundredth.
nCr (6,2) * nCr (5,2) = 150
Total nCr (11,4) = 330
P(Blue and Red balls) = 5/11 or .45
Ian randomly selects a number between 1 and 50. What is the probability that the number selected is the square of a natural number?
Hint: Natural numbers are the counting numbers.
7/50
In a deck of cards what is the probability of picking a 9 or a spade?
4/52 + 13/52 - 1/52 = 16/52
Maurice is going to draw two cards from a standard deck without replacement. What is the probability that the first card is a jack and the second card is a two?
4/52 x 4/51 = 16/2652 = 4/663
In a relay race, the probability of the Sun Devils team winning is 37%. In another unrelated relay race, the probability of the Rajin Cajun team winning is 55%. If the possibility of a tie is not an option, the probability of the Rajin Cajun's losing their race and the Sun Devils winning theirs is ___
(1-0.55)*0.37 = 0.1665 = 16.65%
A box contains 20 lightbulbs, of which 5 are defective. If 4 lightbulbs are picked from the box randomly, the probability that at most 2 of them are defective is ____.
938/969
A six-sided fair die is rolled 5 times in a row. The probability of getting a 2 only on the first trial is _____.
(5*1*5*5*5) / (5*5*5*5*5) = 625/3125 = 1/5
Two cards are drawn from a well-shuffled standard deck of cards. What is the probability of drawing a 6 or a 7 followed by a jack or an ace, with replacement?
Reggie rolled a die 2 times. What is the probability that he rolled a 6 on the first roll, and a 5 on the second roll?
1/6 x 1/6 = 1/36
The probability that Annabelle will study this week is 0.95, and the probability that Anna will study this week is 0.8. The probability that Annabelle and Anna both study this week is 0.76. Are these events dependent? Why?
The events are Independent because P(A) * P(B) = P(A and B).
Suppose that 3 boys and 2 girls go to the theater and occupy 5 seats in a row. In how many ways can they be seated if all 3 boys sit together?
36
The number of three-digit numbers with distinct digits that can be formed using the digits 1, 2, 3, 5 is _____. The probability that both the first digit and second digit of the number are odd numbers is _____.
4 * 3 * 2 = 24
(3*2*1)/24 = 6/24 = 1/4
A survey of the people in a certain town showed that 42% have blond hair and 12% of them have blond hair and blue eyes.
The probability that a randomly selected person has blue eyes, given that they have blond hair, is
P(A) = 42%
P(A and B) = 12%
P(B|A) = .12/.42 = 0.29
Mike has 2 black hats, 1 green hat, and 5 red hats. If he randomly pulls out two hats one after the other without replacement, what is the probability he pulls out two red hats?
5/8 x 4/7 = 20/56
Events X and Y are independent events. If P(X) = 0.55 and P(X and Y) = 0.22, then P(Y) = ____
0.4
There are 6 girls and 7 boys in a class. A team of 10 players is to be selected from the class. How many different combinations of players are possible?
286
An experiment consists of tossing a coin and drawing a card, with the card-drawing stage dependent on the result of the coin toss. If heads occurs, then a card is selected at random from the clubs and spades suits. If tails occurs, then a card is selected at random from the hearts and diamonds suits. What is the size of the sample space of this two-stage experiment?
52
On New Year’s Eve, the probability of a person driving while intoxicated is 0.32, the probability of a person having a driving accident is 0.09, and the probability of a person having a driving accident while intoxicated is 0.06. What is the probability of a person driving while intoxicated or having a driving accident?
P(intoxicated or accident) = P(intoxicated) + P(accident) - P(intoxicated and accident)= 0.32 + 0.09 - 0.06 = 0.35
The probability that Sam parks in a no-parking zone and gets a parking ticket is 0.06, and the probability that Sam cannot find a legal parking space and has to park in the noparking zone is 0.20. On Tuesday, Sam arrives at school and has to park in a no-parking zone. Find the probability that he will get a parking ticket.
0.06 / 0.2 = 0.3
In a factory, the chance that a certain machine works without overheating in the morning is 50%. If it runs smoothly all morning, then there is an 85% chance that it will continue for the rest of the day and a 15% chance that it will stop due to overheating. What is the probability that on a given day it will work in the morning and overheat later on?
7.5%
A group of 8 friends (5 girls and 3 boys) plans to watch a movie, but they have only 5 tickets. If they randomly decide who will watch the movie, what is the probability that there are at least 3 girls in the group that watch the movie?
0.821