STAT 113 Week 8 (Feb 25) Work Sheet 5: Chapter 17, 18 & 20 Probability model and expected value The probability distribution for a game of tossing a fair coin 4 times and recording the number of heads is: outcome No heads 1 head 2 heads 3 heads 4 heads probability 1/16 4/16 6/16 4/16 ? What must be the probability of 4 heads? 1-1/16-4/16-6/16-4/16=1/16=0.0625 (b) What's the probability of getting at 2 heads in this game? sum up the probabilities: 6/16+4/16+1/16=11/16=0.6875 or subtract from total: 1-1/16-4/16=11/16=0.6875 (c) Write out 3 reasons why this is a legitimate probability model: 1. Every possible outcome is listed. 2. Each individual probability is between 0 and 1. 3. All the probabilities added together total to 1. (d) What‘s the expected number of heads when we toss a fair coins 4 times? 0(1/16)+1(4/16)+2(6/16)+3(4/16)+4(1/16) = 2 A deck of cards contains 52 cards, of which 4 are aces. Also there are four different suits in a deck of 52 cards, 13 cards for each (spade, club, heart, and diamond). Randomly draw one card from 52. (a) What's the probability of drawing an ace? 4/52=0.0769 (b) What's the probability of drawing a spade? 13/52=0.25 (c) What's the probability of drawing a diamond or a club? 26/52=0.5 (d) What's the probability of not drawing a 1-13/52=0.75 (e) You win $100 if the card drawn is a 10, and you lose $10 if the card drawn is not a 10. What are your expected winnings?
STAT 113 Week 8 (Feb 25) Work Sheet 5: Chapter 17, 18 & 20 Probability model and expected value The probability distribution for a game of tossing a fair coin 4 times and recording the number of heads is: outcome No heads 1 head 2 heads 3 heads 4 heads probability 1/16 4/16 6/16 4/16 ? What must be the probability of 4 heads? 1-1/16-4/16-6/16-4/16=1/16=0.0625 (b) What's the probability of getting at 2 heads in this game? sum up the probabilities: 6/16+4/16+1/16=11/16=0.6875 or subtract from total: 1-1/16-4/16=11/16=0.6875 (c) Write out 3 reasons why this is a legitimate probability model: 1. Every possible outcome is listed. 2. Each individual probability is between 0 and 1. 3. All the probabilities added together total to 1. (d) What‘s the expected number of heads when we toss a fair coins 4 times? 0(1/16)+1(4/16)+2(6/16)+3(4/16)+4(1/16) = 2 A deck of cards contains 52 cards, of which 4 are aces. Also there are four different suits in a deck of 52 cards, 13 cards for each (spade, club, heart, and diamond). Randomly draw one card from 52. (a) What's the probability of drawing an ace? 4/52=0.0769 (b) What's the probability of drawing a spade? 13/52=0.25 (c) What's the probability of drawing a diamond or a club? 26/52=0.5 (d) What's the probability of not drawing a 1-13/52=0.75 (e) You win $100 if the card drawn is a 10, and you lose $10 if the card drawn is not a 10. What are your expected winnings?
worksheet05_chapter17_18_20_key.docx