Conditional Probability - Page 3
Questions
- From a standard deck, what are the probabilities of A. picking a red card, B. picking a spade, C. picking an Ace?
- The probability that you are late to school is 0.05 for any day. Given that you slept late, the probability that you are late to school is 0.13. Are the events "Late to School" and "Slept Late" independent or dependent?
- A bowl contains 7 pennies, 9 nickels, and 4 dimes. Elyse removes one coin at random from the bowl and does not replace it. She then removes a second coin at random. What is the probability that both will be dimes?
- What is the probability that the sum of two dice rolls is 12 if the sum is even?
- How do you apply Bayes' theorem to continuous random variables?
- What general form of the mass function of a conditional probability distribution for discrete random variables?
- If P(A) = 0.1, P(B) = 0.9, and P(A#nn#B)=0, what is P(B|A)? What about P(A|B)?
- If P(A) = 0.8, P(B) = 0.9, and P(A#nn#B)=.8, what is P(B|A)? What about P(A|B)?
- If #P(A) = 0.7, P(B) = 0.9# and #P(A nn B)=.4#. What is #P(B|A)#? What about #P(A|B)#?
- If P(B|A) = 0.6 and P(A) = 0.5, what is P(B)?
- A bag contains 9 red marbles and 3 green marbles. How can you find the probability of drawing first one green marble and then one red marble if you do not replace the first marble?
- There are two boxes - one holds 11 cards numbered 1 through 11, the other 5 cards numbered 1 through 5. Two cards are randomly drawn. What is the probability of drawing 2 even cards in a row?
- Assume that A and B are events in a sample space and that P(A) = .40 and P(B|A) = .25. How do you find P(A intersection B)?
- I have two servers at a grocery store. P(server 1) is 0.4. P(server 2) is 0.6. P(time is less than 5 min | server 1) is 1. P(time is less than 5 min | server 2) is 4/9. What is P(server 1 | time is less than 5 min)?
- A factory has three machines, A, B, and C, for producing items. Machine A produces 50%, B produces 30%, and C produces 20%. If a randomly selected item from the factory's output is found to be defective, what is the probability that B made it?
- Batches of serum are processed by three different departments having rejection rates of 0.10, 0.08, and 0.12 respectively. What is the probability that a batch of serum survives the first departmental inspection but is rejected by the second department?
- The probability of having a toothache because of a cavity is 0.8. Suppose the probability of having a cavity is 0.05. Assuming the probability of a toothache given you have no cavity is 0.01, what's 'the probability of a cavity if you have a toothache?
- Among the contestants in a competition are 42 women and 28 men. If 5 winners are randomly selected, what is the probability that they are all men?
- In a string of 12 christmas lights, 3 are defective. Bulbs are selected at random, one at a time, until the third defective bulb is found. What is the probability that the third defective bulb is the third bulb tested?
- Ron draws 16 cards from a standard deck of 52. The deck is made up of equal numbers of four suits clubs diamonds, hearts, and spades. How many of the cards drawn can Ron expect to be spades?