A RANDOM REAL FROM A RANGE
Select : Random Real [Lower, Upper]
Select : Random Integer [Lower,Upper]
A RANDOM SELECTION OF VALUES
Select : Random Sample (k items)
A RANDOM INTEGER FROM A RANGE
A RANDOM INTEGER BETWEEN 0 & YOUR CHOICE
Select : Random Integers [0. Upper]
A RANDOM REAL BETWEEN 0 & YOUR CHOICE
Select : Random Real [0.0, Upper]
A RANDOM REAL FROM 0.0 to 1.0
Select : Random Real [0.0,1.0]
A RANDOM 0 or 1
Select : Random 0 or 1]
A COIN FLIP
Select : Coin Flip]
A RANDOM ROLL OF DICE
Select : Dice Rolls]
This page highlights just a few of the equations on vCalc that demonstrate the application of Probability.
We'll look at probability applied to happiness, to card games like Poker, to random choices, to the search for life beyond our solar system.
NOTE: many vCalc equations are embedded throughout vCalc descriptive pages like this page. Even though they may not stand out in the text, if you hover over the name of an equation it will likely be linked to an actual, pop-up executable equation. For example: Arithmetic Mode
org.xwiki.properties.PropertyException: Failed to populate property [depth] at org.xwiki.properties.internal.DefaultBeanManager.populateBean(DefaultBeanManager.java:172) at org.xwiki.properties.internal.DefaultBeanManager.populate(DefaultBeanManager.java:109) at org.xwiki.rendering.internal.transformation.macro.MacroTransformation.transform(MacroTransformation.java:287) at com.vcalc.uil.Util.convertWiki(Util.java:502) at com.vcalc.uil.Util.convertWiki(Util.java:599) at com.vcalc.uil.util.VCHtml.getContent(VCHtml.java:51) at org.zkoss.zul.Html.renderProperties(Html.java:121) at org.zkoss.zk.ui.AbstractComponent.redraw(AbstractComponent.java:2180) at org.zkoss.zk.ui.AbstractComponent.redrawChildren(AbstractComponent.java:2271) at org.zkoss.zk.ui.AbstractComponent.redraw(AbstractComponent.java:2212) at org.zkoss.zk.ui.AbstractComponent.redrawChildren(AbstractComponent.java:2271) at org.zkoss.zk.ui.AbstractComponent.redraw(AbstractComponent.java:2212) at org.zkoss.zk.ui.AbstractComponent.redrawChildren(AbstractComponent.java:2271) at org.zkoss.zk.ui.AbstractComponent.redraw(AbstractComponent.java:2212) at org.zkoss.zk.ui.AbstractComponent.redrawChildren(AbstractComponent.java:2271) at org.zkoss.zk.ui.AbstractComponent.redraw(AbstractComponent.java:2212) at org.zkoss.zk.ui.sys.HtmlPageRenders.outPageContent(HtmlPageRenders.java:684) at org.zkoss.zul.impl.PageRenderer.renderDesktop(PageRenderer.java:99) at org.zkoss.zul.impl.PageRenderer.render(PageRenderer.java:56) at org.zkoss.zk.ui.impl.PageImpl.redraw(PageImpl.java:944) at org.zkoss.zk.ui.impl.UiEngineImpl.execNewPage0(UiEngineImpl.java:576) at org.zkoss.zk.ui.impl.UiEngineImpl.execNewPage(UiEngineImpl.java:367) at org.zkoss.zk.ui.http.DHtmlLayoutServlet.process(DHtmlLayoutServlet.java:211) at org.zkoss.zk.ui.http.DHtmlLayoutServlet.doGet(DHtmlLayoutServlet.java:146) at javax.servlet.http.HttpServlet.service(HttpServlet.java:687) at javax.servlet.http.HttpServlet.service(HttpServlet.java:790) at org.eclipse.jetty.servlet.ServletHolder$NotAsync.service(ServletHolder.java:1443) at org.eclipse.jetty.servlet.ServletHolder.handle(ServletHolder.java:791) at org.eclipse.jetty.servlet.ServletHandler.doHandle(ServletHandler.java:550) at org.eclipse.jetty.server.handler.ScopedHandler.handle(ScopedHandler.java:143) at org.eclipse.jetty.security.SecurityHandler.handle(SecurityHandler.java:602) at org.eclipse.jetty.server.handler.HandlerWrapper.handle(HandlerWrapper.java:127) at org.eclipse.jetty.server.handler.ScopedHandler.nextHandle(ScopedHandler.java:235) at org.eclipse.jetty.server.session.SessionHandler.doHandle(SessionHandler.java:1624) at org.eclipse.jetty.server.handler.ScopedHandler.nextHandle(ScopedHandler.java:233) at org.eclipse.jetty.server.handler.ContextHandler.doHandle(ContextHandler.java:1435) at org.eclipse.jetty.server.handler.ScopedHandler.nextScope(ScopedHandler.java:188) at org.eclipse.jetty.servlet.ServletHandler.doScope(ServletHandler.java:501) at org.eclipse.jetty.server.session.SessionHandler.doScope(SessionHandler.java:1594) at org.eclipse.jetty.server.handler.ScopedHandler.nextScope(ScopedHandler.java:186) at org.eclipse.jetty.server.handler.ContextHandler.doScope(ContextHandler.java:1350) at org.eclipse.jetty.server.handler.ScopedHandler.handle(ScopedHandler.java:141) at org.eclipse.jetty.server.handler.HandlerList.handle(HandlerList.java:59) at org.eclipse.jetty.server.handler.HandlerWrapper.handle(HandlerWrapper.java:127) at org.eclipse.jetty.server.Server.handle(Server.java:516) at org.eclipse.jetty.server.HttpChannel.lambda$handle$1(HttpChannel.java:388) at org.eclipse.jetty.server.HttpChannel.dispatch(HttpChannel.java:633) at org.eclipse.jetty.server.HttpChannel.handle(HttpChannel.java:380) at org.eclipse.jetty.server.HttpConnection.onFillable(HttpConnection.java:273) at org.eclipse.jetty.io.AbstractConnection$ReadCallback.succeeded(AbstractConnection.java:311) at org.eclipse.jetty.io.FillInterest.fillable(FillInterest.java:105) at org.eclipse.jetty.io.ChannelEndPoint$1.run(ChannelEndPoint.java:104) at org.eclipse.jetty.util.thread.strategy.EatWhatYouKill.runTask(EatWhatYouKill.java:336) at org.eclipse.jetty.util.thread.strategy.EatWhatYouKill.doProduce(EatWhatYouKill.java:313) at org.eclipse.jetty.util.thread.strategy.EatWhatYouKill.tryProduce(EatWhatYouKill.java:171) at org.eclipse.jetty.util.thread.strategy.EatWhatYouKill.run(EatWhatYouKill.java:129) at org.eclipse.jetty.util.thread.ReservedThreadExecutor$ReservedThread.run(ReservedThreadExecutor.java:375) at org.eclipse.jetty.util.thread.QueuedThreadPool.runJob(QueuedThreadPool.java:773) at org.eclipse.jetty.util.thread.QueuedThreadPool$Runner.run(QueuedThreadPool.java:905) at java.base/java.lang.Thread.run(Thread.java:829) Caused by: java.lang.NullPointerException at org.apache.commons.lang3.SystemUtils.isJavaVersionAtLeast(SystemUtils.java:1371) at org.apache.commons.lang3.ClassUtils.isAssignable(ClassUtils.java:589) at org.apache.commons.lang3.reflect.TypeUtils.isAssignable(TypeUtils.java:131) at org.apache.commons.lang3.reflect.TypeUtils.isAssignable(TypeUtils.java:80) at org.apache.commons.lang3.reflect.TypeUtils.isAssignable(TypeUtils.java:65) at org.xwiki.properties.internal.converter.ConvertUtilsConverter.convert(ConvertUtilsConverter.java:84) at org.xwiki.properties.internal.converter.ConvertUtilsConverter.convert(ConvertUtilsConverter.java:105) at org.xwiki.properties.internal.DefaultConverterManager.convert(DefaultConverterManager.java:114) at org.xwiki.properties.internal.DefaultBeanManager.populateBean(DefaultBeanManager.java:154) ... 59 more
Here are some probabilities that apply to the game of Poker and drawing cards from a regular deck of 52 cards :
Here are some uncommon ways that probability is used:
How many times have you seen or heard someone suggest that a random event is "due" to occur. An ignorant gambler flipping a coin will sometimes remark that because quite a number of heads have come up in a row that a heads is "due". The fact is that each and every flip of the coin has precisely the same probability of turning up a heads. The random flip could quite literally result in 1000 straight heads and the probability of the very next flip producing a tails will again be exactly 1/2.
Similarly, people who play the Powerball every week believing their chance will improve over time are essentially, unmistakably wrong. The probability resets each time the numbers are drawn and next week the probability is the same. CLICK HERE to see the embarrassingly minuscule probability Powerball players are paying out money weekly for.
The iconic die that have six sides, numbers 1 through six from which you can roll lucky sevens or "snake eye" are but one of many dice that you can find being used in play today. Any regular polyhedral will roll like a dice. CLICK HERE to try vCalc's Dice Rolls calculator that allows you to roll numbers from a set of multi-sided dice. There are easily producible dice with sides for each different polyhedron that are all polygons with the same dimensions.
In other words the tetrahedron has sides that are all equilateral triangles, the cube has sides that are equal squares, the octahedron has again sides that are equilateral triangles, the dodecahedron has sides that are regular pentagons, and the icosahedron has sides which are equilateral triangles:
vCalc includes the following "virtual dice" from which you can roll random numbers from other than 4, 6, 8, 12 or 20 sided physical dice and you can roll multiple dice at the same time: