Probability And Counting Techniques Flashcards
What does the Fundamental Counting Principal allow us to do?
It allows us to count the number of ways a task can occur given a series of events?
How can probability trees be used?
Probability trees can be used to compute the probabilities of combined outcomes in a sequence of experiments.
A shipment of 500 DVD players contains 9 defective DVD players. Construct the probability of the experiment of sampling two of them without replacement.
How many leaves does the tree have? What are their probabilities?
4 leaves
8/499, 491/499, 9/499, 490/499
The faculty of a college consists
of 65 male faculty and 35 female faculty. 70% of the female faculty favor raising tuition, while only 40% of male faculty favor the increase. If a faculty member is selected at random from this group, what is the probability that he or she favors raising tuition?
Can you use a probability tree to solve this problem? If so, how many leaves are there and what are their probabilities?
P(raise tuition) = .505
4 leaves
.245, .105, .26, .39
A store has 80 modems in its inventory, 30 coming from Source A and the remainder from Source B. Of the modems from Source A, 20% are defective. Of the modems from Source B, 8% are defective. Calculate the probability that exactly two out of a random sample of 5 modems from the stores inventory are defective.
Can you use a probability tree to solve this problem?
.102
Yes.
From 27 pieces of luggage, an airline luggage handler damages a random sample of four. The probability that exactly one of the damaged pieces of luggage is insured is twice the probability that none of the damaged pieces are insured. Calculate the probability that exactly two of the damaged pieces are insured.
Can you use a probability tree?
.27
Yes.
A box contains three red balls and two blue balls. Two balls are to be drawn without replacement. Use a tree diagram to represent the various outcomes that can occur. What is the probability of each outcome?
3/10, 3/10, 3/10, 1/10
Consider a jar with three black marbles and one red marble. For the experiment of drawing two marbles with replacement, what is the probability of drawing a black marble and then a red marble in that order? Assume that the balls are equally likely to be drawn.
.1875
A board of trustees of a university consists of 8 men and 7 women. A committee of 3 must be selected at random and without replacement. Calculate the probability that the number of men selected exceeds the number of women selected.
36/65 or .5538
