Math 107 CH 7 Test - Deeney
Find the probability of at least one queen when you draw cards from a standard deck 5 times; assume you replace the card each time you draw, so there are always 52 cards to draw from.
1- P(no queen in 5 draws) 1- [P(not queen)]^4 1-[48/52]^4 = .273975009 = 27/100 ish
Expected value equation
( Event 1 value) x ( Event 1 probability) + ( Event 2 value) x (Event 2 probability)
Find the probability of correctly answering the first 3 questions on a multiple choice test if random guesses are made and each question has 6 possible answers.
(1/6)(1/6)(1/6)=1/216
A sample of 4 different calculators is randomly selected from a group containing 45 that are defective and 26 that have no defects. What is the probability that all four of the calculators selected are defective?
(45/71)(44/70)(43/69)(42/68)= 3,575,880/20,575,800
Of the 43 people who answered "yes" to a question, 9 were male. Of the 41 people who answered "no" to the question, 7 were male. If one person is selected at random from the group, what is the probability that the person answered "yes" or was male?
50/84
You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that both cards are black.
52 cards per deck. 13 cards of each suit. two suits are black. 26 black cards in a deck. probability of getting a black card the first time you draw is 26/52. Since you don't put that card back in the deck there are now 51 cards total and since you got a black card in your first draw there are now 25 black ones left. Probability of getting a black card the next time you draw is 25/51. (26/52)(25/52) = 650/2,704
Law of large numbers
If the expected probability of getting heads when flipping a coin is 50% then, the law of large numbers says that the more times you flip the coin, the closer the number of heads flipped will be to 50% of the time. Example: If you flip the coin ten times you might get 8 heads and 2 tails. However, if you flip 100,000,000,000 coins, you will likely get fairly close to 50% of the results as heads so you might end up getting somewhere around 50,000,652,989 heads.
Theoretical Probability
It is the likeliness of an event happening based on all the possible outcomes. The ratio for the probability of an event 'P' occurring is P (event) = number of favorable outcomes divided by number of possible outcomes. P(A) = number of ways A can occur/ total number of outcomes
At least once rule
P( At least one event A in N trials ) = 1 -P( not event A in n trials) = [P( not A in one trial)]^n
Probability Equation for Dependent Events
P(A and B)= P(A) x P(B given A)
Probability Equation for Independent Events
P(A and B)= P(A) x P(B)
Either/or Probability Equation non-overlapping events
P(A or B)= P(A) + P(B)
Either/or Probability Equation overlapping events
P(A or B)= P(A) + P(B) - P(A and B)
Subjective Probability
Subjective probability is a probability derived from an individual's personal judgment about whether a specific outcome is likely to occur. It contains no formal calculations and only reflects the subject's opinions and past experience.
Empirical Probability
The empirical probability, also known as relative frequency, or experimental probability, is the ratio of the number of outcomes in which a specified event occurs to the total number of trials, not in a theoretical sample space but in an actual experiment. Empirical means " by observation" so if you flip a coin ten times and get seven heads, your empirical probability is 7 in 10.
A fair die is rolled. What is the probability of rolling an odd number or a number less than 3?
odd numbers between 1 and 6 = 1, 3, 5 (three numbers) numbers less than 3= 1, 2 (two numbers) 3 + 2 -1 = 4 (-1 because they overlap) The probability of getting an odd number or a number less than 3 is: 4/6
Two fair 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice is greater than 10?
write out all possibilities. count the possibilities. There are 6 ways to roll two dice to get 10.
