Probability
A bag contains 4 red, 6 blue, and 2 green marbles. What is the probability of randomly selecting a blue marble?
P(blue) = 6/12 = 1/2 = 0.5
Define “mutually exclusive events.”
Events that cannot happen at the same time.
What does P(A|B) mean?
The probability of A happening given that B already happened.
What is the probability of flipping heads twice in a row?
1/2 × 1/2 = 1/4
What does it mean for two events to be independent?
One event happening does not affect the probability of the other.
A standard die is rolled. What is the probability of rolling an even number?
3/6 = 1/2
If P(A)=0.4 and P(B)=0.3 and A and B are mutually exclusive, find P(A or B).
0.7
In a deck of cards, given that the card is red, what is the probability it is a heart?
13/26 = 1/2
A die is rolled twice. What is the probability of rolling two 6’s?
1/6 × 1/6 = 1/36
If P(A)=0.5 and P(B)=0.2 and the events are independent, find P(A and B).
0.5 × 0.2 = 0.10
A bag contains 3 red, 2 blue, and 5 green marbles. What is the probability of drawing a blue marble?
2/10 = 1/5
In a class, 18 students play sports, 12 play instruments, and 5 do both. If there are 30 students total, what is the probability a student plays sports or instruments?
(18+12−5)/30 = 25/30 = 5/6
In a survey, 40 students are freshmen and 15 of those freshmen have allergies. What is P(Allergies|Freshman)?
15/40 = 3/8
29% of internet users download music, and 67% of those users don’t care about copyright. What percent both download music and don’t care?
0.29 × 0.67 = 0.1943 or 19.43%
A heart is drawn, replaced, and another card is drawn. Are the events independent? Explain.
Yes, because replacing the card keeps probabilities the same.
Three fair coins are flipped. What is the probability of getting exactly 2 heads?
3/8
A card is drawn from a deck. Find the probability the card is a heart or a face card.
13/52 + 12/52 − 3/52 = 22/52 = 11/26
A school has 500 students. 310 are graduates and 221 are homeowners who are graduates. Find P(Homeowner|Graduate).
221/310 ≈ 0.713
Shannon hits snooze 60% of the time. If she hits snooze, she is late 30% of the time. If she doesn’t, she is late 10% of the time. Find the probability she is late.
(0.60)(0.30) + (0.40)(0.10) = 0.22
A heart is drawn and NOT replaced, then another card is drawn. Are the events independent? Explain.
No, because the first draw changes the probabilities for the second draw.
A card is drawn from a standard deck. What is the probability of drawing a red face card?
6/52 = 3/26
60% of households have a landline, 89% have a cell phone, and 51% have both. What is the probability a household has neither type of phone?
1 − (0.60 + 0.89 − 0.51) = 0.02
In a factory, 40% of computers come from California and 75% of those are laptops. What is the probability a randomly selected computer is a laptop from California?
0.40 × 0.75 = 0.30
A company makes computers in CA (40%), TX (25%), and NY (35%). Laptop rates are 75%, 70%, and 50%. Find the overall probability a computer is a laptop.
(0.40)(0.75) + (0.25)(0.70) + (0.35)(0.50) = 0.65
A bomber has a 0.95 chance of returning safely from one mission. Assuming independence, what is the probability it returns safely from 20 missions?
(0.95)^20 ≈ 0.3585 or 35.85%