Coin Flipping. Two Dice

Transcription

1 Cin Flipping - Use the randm peratin t write a prgram that flips a cin 10 times and shws hw many were heads and hw many were tails. Divide ne by the ther t see hw clse the rati is 1. Run the prgram several times t see hw the rati changes. What happens t the rati if yu flip 100 times? 1000 times? - If yu like, add graphics t shw the result f each cin flip (but yu ll still have t keep the flipping fast r it will be t bring t wait fr the prgram t flip 100 times). Tw Dice - Use the randm peratin t make a prgram that rlls tw dice and adds up the ttal (a number frm 2 t 12). Keep track f hw many times yu get each number. Yu can keep track using 11 variables, r yu can use a list (ask fr help if yu want t knw hw). Make yur prgram d 10 rlls, then try 100 rlls and 1000 rlls. - Make the prgram draw a bar chart shwing hw many times each number came up. What patterns d yu see? Can yu explain it? - If yu like, add graphics t shw the result f each dice rll. Blackjack - Use the randm peratin t make a prgram that deals tw randm cards frm a deck by picking a randm suit (spades, hearts, diamnds, r clubs) and a randm rank (2, 3, 4, 5, 6, 7, 8, 9 10, J, Q, K, r A). (Can yu make sure the tw cards aren t exactly the same?) Check if the ttal is 21 (ace cunts as 11, and face cards cunt as 10, s yu d need an ace and a 10/J/Q/K). Have yur prgram deal lts f times and keep track f hw many tw-card hands are 21. Make an estimate fr the chance f being dealt a 21 with tw cards - If yu like, add graphics t shw the tw cards.

2 Mnty Hall Puzzle There are three drs. There is a gd prize behind ne f them, and bad prizes behind ther tw. Yu chse a dr (but nbdy pens it yet). Then, Mnty pens ne f the ther tw drs and (very imprtant!) he always picks a dr that reveals ne f the bad prizes he never pens the gd dr. Nw yu have a chice: yu can chse t stick with yur first chice f dr, r yu can switch t the ther dr (the ne f the remaining tw that Mnty didn t pen). The questin is: Is it better t keep yur first chice, switch, r it desn t matter? Example: Suppse in the picture abve yu are tld there is a car behind ne f the three drs. Yu guess dr #2. Mnty says that he ll pen ne f the ther drs, and the dr he ll pen has a bad prize. He pens dr #3 and indeed it has a bad prize (assuming yu dn t want a gat). The questin is: Shuld yu change yur guess t dr #1, r leave it at dr #2, r des it nt matter? Write a cmputer simulatin t find ut!

3 Randm Maze Escape - Draw a simple maze n the backgrund using a certain clr. Make a sprite pick a directin: up, dwn, left, r right. The sprite mves 10 pixels at a time in that directin. If it hits a wall, it backs up 10 and chses anther randm directin and keeps repeating. Can the sprite get ut f yur maze? Balls and Urn Yu are given tw urns (cntainers like big vases) and 5 black balls and 5 white balls. Smebdy else will cme in and pick ne f the urs at randm and a ball drawn at randm frm it. If the ball they pick is white, yu win. If the ball they pick is black, yu lse. Hw wuld yu distribute the balls s as t maximize the chances f winning? Write a prgram that tries a distributin (e.g., urn1 has 2 black and 3white, urn2 has 2 white and 3 black) and figures ut the prbability f the persn picking a white by simulating lts f times. Try varius distributins and see which ne wrks best.

4 Fill Squares - Make a prgram that fills a 10x10 grid with clred squares. Yu can d this using a square sprite whse clr yu change randmly (it desn t matter what the clrs are fr this experiment; yu can use all the same clr r use different clrs t make a nice picture like the ne abve). Repeatedly pick a randm x value frm 0 t 9 and a y randm value frm 0 t 9 and draw a square at that grid lcatin. Keep cunt f hw many squares yu plt. Watch the prgram and stp it by pressing a key when all squares in the grid have been filled. Hw many tries des it take t fill the screen? D it lts f times and see hw many tries it takes n average. Pachink Machine

5 Pker Hands - Make a prgram that uses randm t deal a 5-card pker hand. Check if yur hand has at least a pair. Keep track f hw many times yu get at least a pair. Give an estimate f the prbability f getting dealt at least a pair. - Yu can add ther pker hand types and see what the chances f getting thse are see the chart abve. - If yu like, add graphics t shw the five cards.