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<html><table height="500" width="1000" border="2"><TR height="5" width="1000"><strong><center><marquee><font color="Green"><h1>APTITUDE</h1></center></strong></font></TR></marquee><TR><TD align="left" width="200" valign="top"><table><TR><a href="numbers.html"><strong>Numbers</strong></a></TR><br><TR><a href="hcf.html"><strong>H.C.F and L.C.M</strong></a></TR><br><TR><a href="dec.html" target="right"><strong>Decimal Fractions</strong></a></TR><br><TR><a href="simplification.html"><strong>Simplification</strong></a></TR><br><TR><a href="squareandcuberoot.html" target="right"><strong>Square and Cube roots</strong></a></TR><br><TR><a href="average.html" ><strong>Average</strong></a></TR><br><TR><a href="pnumbers.html" ><strong>Problems on Numbers</strong></a></TR><br><TR><a href="problemsonages.html"><strong>Problems on Ages</strong></a></TR><br><TR><a href="surdsandindices.html"><strong>Surds and Indices</strong></a></TR><br><TR><a href="percent.html" target="right"><strong>Percentage</strong></a></TR><br><TR><a href="profitandloss.html" target="right"><strong>Profit and Loss</strong></a></TR><br><TR><a href="ratioandproportion.html" target="right"><strong>Ratio And Proportions</strong></a></TR><br><TR><a href="partnership.html"><strong>Partnership</strong></a></TR><br><TR><a href="chainrule1.html"><strong>Chain Rule</strong></a></TR><br><TR><a href="timeandwork.html" target="right"><strong>Time and Work</strong></a></TR><br><TR><a href="pipesandcisterns.html" target="right"><strong>Pipes and Cisterns</strong></a></TR><br><TR><a href="timeanddistance.html"><strong>Time and Distance</strong></a></TR><br><TR><a href="trains.html" target="right"><strong>Trains</strong></a></TR><br><TR><a href="boats.html"><strong>Boats and Streams</strong></a></TR><br><TR><a href="alligation.html"><strong>Alligation or Mixture </strong></a></TR><br><TR><a href="simple.html" target="right"><strong>Simple Interest</strong></a></TR><br><TR><a href="CI.html" target="right"><strong>Compound Interest</strong></a></TR><br><TR><a href=""><strong>Logorithms</strong></a></TR><br><TR><a href="areas.html" target="right"><strong>Areas</strong></a></TR><br><TR><a href="volume.html" target="right"><strong>Volume and Surface area</strong></a></TR><br><TR><a href="races.html" target="right"><strong>Races and Games of Skill</strong></a></TR><br><TR><a href="calendar.html" target="right"><strong>Calendar</strong></a></TR><br><TR><a href="clocks.html" target="right"><strong>Clocks</strong></a></TR><br><TR><a href="" target="right"><strong>Stocks ans Shares</strong></a></TR><br><TR><a href="true.html" target="right"><strong>True Discount</strong></a></TR><br><TR><a href="banker1.html" target="right"><strong>Bankers Discount</strong></a></TR><br><TR><a href="oddseries.html" target="right"><strong>Oddmanout and Series</strong></a></TR><br><TR><a href=""><strong>Data Interpretation</strong></a></TR><br><TR><a href="probability.html"><strong>probability</strong></a></TR><br><TR><a href="percom1.html" target="right" ><strong>Permutations and Combinations</strong></a></TR><br><TR><a href="pinkivijji_puzzles.html" target="right"><strong>Puzzles</strong></a></TR></table></TD><TD valign="top"><a href="probability.html"><b>BACK</b></a><br><br><font size="5"><b><center>PROBABILITY</center></b></font><br><br><br><br> <font size="4"><b>EXPERIMENT:</b>An operation which can produce some well-defined outcome is called an experiment.<br><br><b>RANDOM EXPERIMENT</b> : An experiment in which all possible out comes are known and<br> the exact output cannot be predicted in advance is called a random experiment.<br><b>EX:</b><br> 1) Rolling an unbiased dice.<br> 2) Tossing a fair coin.<br> 3) Drawing a card from a pack of well-shuffled cards .<br>4)Picking up a ball of certain colour from a bag containing balls of different<br> colours.<br><br><b>DETAILS:</b><br> 1) When we thrown a coin ,then either a Head(H) or a Tail(T) appears.<br>2)A dice is a solid cube ,having 6 faces,marked 1,2,3,4,5,6 respectively.<br>When we throw a die ,the outcome is the number that appears on its upper face.<br>3)A pack of cards has 52 cards.<br>It has 13 cards of each suit,namely spades,clubs,hearts and diamonds.<br>Cards of spades and clubs are balck cards.<br>Cards of hearts and diamonds are red cards.<br>There are four honours of each suit.<br>These are Aces,Kings,queens and Jacks.<br>These are called Face cards.<br><br><b>SAMPLE SPACE:</b>When we perform an experiment ,then the set of S of all possible<br> outcomes is called the Sample space .<br><b>EX:</b><br>1)In tossing a coin S= {H,T}.<br>2)If two coins are tossed then S= {HH,HT,TH,TT}.<br>3)In rolling a dice ,we have S={1,2,3,4,5,6}.<br><br><br><b>EVENT</b>: Any subset of a sample space is called an Event.<br><br>Probability of occurrence of an Event:<br> Let S be the sample space.<br> Let E be the Event.<br> Then E cS i.e E is subset of S then<br>probability of E p(E) =n(E)/n(S).<br><br><br>Reults on Probability:<br>1)P(S) =1.<br>2)0 < P(E) < 1<br>probability of an event lies between 0 and 1.<br>Max value of probability of an event is one.<br>3)P(Ф)=0.<br>4)For any events A and B we have .<br>P(AUB) =P(A) +P(B) -P(AnB).<br>5)If A denotes (not -A) then<br>P(A) =1-P(A)<br>P(A)+P(A) =1.<br><br><br><a href="probability.html"><b>BACK</b></a></TD></TR></table></html>?? 快捷鍵說明
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