Sample Space &
The Addition Rule
The Addition Rule
The probability of both the first & last digit in a distinct 4 digit number being even from {1, 2, 3, 5, 8, 9}.
1/15
In a game of darts, the probability that he throws a dart into the Bull’s eye is 0.05. The probability that he throws the dart into the 10-point ring is 0.2. What is the probability that he either hits a Bull’s eye or scores 10 points?
0.25
The probability of event A is 0.73 and the probability of event B is 0.61. The probability of both is 0.4453. Are events A and B independent?
Yes they are independent because P(A and B)= P(A)*P(B)
A container holds 50 electronic components, of which 10 are defective. If 6 components are drawn at random from the container, the probability that at least 4 are not defective is __A__. If 8 components are drawn at random from the container, the probability that exactly 3 of them are defective is __B__.
A=0.91
B=0.147
Remember this on the test!
P(A|B)=.32
P(A and B)= .13
What is P(B)?
0.406
25/216
In a relay race, the probability of team A winning is 32%. In another unrelated relay race, the probability of team B winning is 37%. If the possibility of a tie is not an option, what is the probability of team A losing their race and team B winning theirs?
0.2516
Events M and N are not independent events. In this scenario, if P(M) = 0.4 and P(M and N) = 0.2, then P(N) cannot equal what?
0.5
Betty picks 4 random marbles from a bowl containing 3 white, 4 yellow, and 5 blue marbles. What is the probability that exactly 1 of the 4 marbles drawn is blue?
0.3535
A printer needs two new ink cartridges. One cartridge lasts 5 years and the other lasts 10 years. The spec sheet says the chance of ink failure after 5 years is 7% and increases to 12% after 10 years. If the cartridges are independent of each other, what is the probability of both ink cartridges failing?
0.0084 or 0.84%
A random number between 1-100 is picked. What is the probability the number is a multiple of 10?
1/10
If P(A|B)= 0.7 and P(A)=0.4 is A independent of B?
No, if A were independent of B, P(A|B)=P(A).
If A and B are independent events, is this statement True or False?
P(A and B)=P(A)+P(B)
False
Betty picks 4 random marbles from a bowl containing 3 white, 4 yellow, and 5 blue marbles. What is the probability that at least 1 of the 4 marbles drawn is white?
0.7455
Two non-simultaneous events have 40% and 30% likelihood of occuring. If the events are independent of each other, what is the probability they will both occur?
0.12 or 12%
There are two grocery stores in town. A survey shows 75% of the residence choose the first store, while 68% prefer the second store, and 58% visit both stores. What is the probability a residence shops at either the first OR second store?
85%
True or False? P(A and B)=P(B|A) * P(A)
True
If P(A)=0.67 and P(A and B)=0.536, what does P(B) if A and B are independent?
0.8
A classroom has 25 seats, with 5 rows of 5 seats. 15 students from the first grade and 5 students from the second grade sit in the classroom. How many ways can the students be seated if all of the second-grade students occupy the first row?
2.432 x 10^18
What is the probability of drawing a 5 and then a 6, with replacement, in a deck of cards?
1/169
An ice cream store sells chocolate, vanilla, or chocolate/vanilla twist ice cream. The probability of picking vanilla only is 0.3, chocolate only is 0.4, and twist is 0.2. What is the probability a customer will pick neither?
0.1
What is the probability of drawing a queen followed by a king, with replacement?
1/169
If A and B are dependent events, is this statement True or False?
P(B|A)!=(B)
True
A classroom has 25 seats, with 5 rows of 5 seats. 15 students from the first grade and 5 students from the second grade sit in the classroom. How many ways can the students be seated if all the first-grade students occupy the first 3 rows?
3.954 x 10^16
What is the probability of drawing a jack followed by a spade, with replacement, in a deck of cards?
1/52