1 / 12

Ch. 19- Probability Day 1

Ch. 19- Probability Day 1. Ex. 1 Pat keeps records on how often she fills her car with petrol. The table shows the frequencies of the number of days between refills . Estimate the likelihood that: a) there is a four day gap between refills

mguerin
Download Presentation

Ch. 19- Probability Day 1

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Ch. 19- Probability Day 1

  2. Ex. 1 Pat keeps records on how often she fills her car with petrol. The table shows the frequencies of the number of days between refills. Estimate the likelihood that: a) there is a four day gap between refills b) there is at least a four day gap between refills. She refilled the car a total of 190 times. There was a four day gap between refills a total of 17 refills. a) Probability = 17/190 At least a four-day gap includes, 4,5, or 6 day gaps. So: b) Probability = (17+6+1)/190 = 24/190

  3. A sample space is the set of all possible outcomes of an experiment. Ex. 2 List the sample space of possible outcomes for: a) tossing a coin b) rolling a die a) Two possible outcomes: b) 6 possible outcomes: Ex. 3 Illustrate the possible outcomes when 2 coins are tossed by using a 2-dimensional grid: coin 1 H T H T coin 2 Each of these points represents one of the possible outcomes in the sample space of tossing two coins:

  4. Ex. 4 Illustrate, using a tree diagram, the possible outcomes when: • tossing two coins • drawing two marbles from a bag, containing several red, green, and • yellow marbles coin 1 coin 2 Each branch represents a possible outcome: H T H T a) H T marble 1 marble 2 R G Y R G Y We could repeat these branches as many times as needed for marbles 3, 4, etc… b) R G Y Tree diagrams are very important and will be used often in solving probability problems! R G Y

  5. Ex. 5 A ticket is randomlyselected from a basket containing 3 green, • 4 yellow, and 5 blue tickets. Determine the probability of getting: • a green ticket b) a green or yellow ticket • c) an orange ticket d) a green, yellow, or blue ticket The sample space is: = 12 outcomes a) P(G) = 3/12 = 1/4 b) P(G or Y) = 7/12 c) P(O) = 0 d) P(G,Y, or B) = 1

  6. In the last problem, an orange ticket had a probability of 0. The probability of getting a green, yellow, or blue ticket was 1. For any event E, Ex. 6 An ordinary 6-sided die is rolled once. Determine the chance of: • getting a 6 b) not getting a 6 • c) getting a 1 or 2 d) not getting a 1 or 2 a) P(6) = 1/6 b) P(not 6) = 5/6 These are complimentary events. Notice that: P(6) + P(not 6) = 1 c) P(1 or 2) = 2/6 = 1/3 d) P(not 1 or 2) = 4/6 = 2/3

  7. If E is an event, then is the complimentary event of E. P(E not occurring) = 1- P(E occurring)

  8. Ex. 7 Use a two-dimensional grid to illustrate the sample space for tossing a coin and rolling a die simultaneously. From this grid determine the probability of: a) tossing a head b) getting a tail and a 5 c) getting a tail or a 5 coin H T From the grid, you can see there are 12 possible outcomes. 1 2 3 4 5 6 die a) P(H) = 6/12 = 1/2 b) P(T and 5) = 1/12 6 chances of getting a tail (including 5) + 1 chance of getting a 5, that’s not a tail c) P(T or 5) = = 7/12

  9. Independent events are events where the occurrence of one event does not affect the occurrence of the other event. If A and B are independent events, then This can be extended as needed: Dependent events are events where the occurrence of one of the events does affect the occurrence of the other event. If A and B are dependent events, then (More to come on dependent events later…)

  10. Ex. 8 A coin and a die are tossed simultaneously. Determine the probability of getting a head and a 3 without using a grid. First note that these are independent events. P(head and 3) = P(H) x P(3)

  11. Ex. 9 A box contains 4 red and 2 yellow tickets. Two tickets are randomly selected, one by one from the box, without replacement. Find the probability that: a) both are red b) the first is red and the second is yellow a) P(both red) = P(first red and second red) =P(first red) x P(second red) b) P(first red and second yellow) = P(first red) x P(second yellow)

  12. Ex. 10 A hat contains tickets with numbers 1,2,3,…,19,20 printed on them. If 3 tickets are drawn from the hat, without replacement, determine the probability that all are prime numbers. Of the 20 numbers, 8 are prime. We want P(3 primes). =P(prime on 1st draw and prime on 2nd draw and prime on 3rd draw) =P(prime on 1st draw) x P(prime on 2nd draw) x P(prime on 3rd draw)

More Related