Measuring Probability Objectively

Transcript

Measuring Probability Objectively There are two completely different approaches to calculating the probability of an event: Experimental Probability: You actually roll the dice, flip the coin, or collect data in the real world to see what happens Theoretical Probability: You sit back, look at the object (like a coin), use logic to count the possible outcomes, and calculate what should happen in a perfect world Let’s look at it in more detail THEORETICAL PROBABILITY What SHOULD happen based on math． Number of ( event )=" favorable outcomes " /■(" Total possible " @" outcomes " ) Example： ROLLING A 4 ON A DIE －Possible outcomes： 1，2，3，4，5， 6 （Total： 6 ） P(" rolling a " 4)=1/6 EXPERIMENTAL PROBABILITY What ACTUALLY happens based on trials． P(" event ")=■(" Number of times " @" event occurs " )/■(" Total number " @" of trials " ) Example： ROLLING A DIE 50 TIMES －Data Collected： Rolling a 4 happened 10 times in 50 trials P(" rolling a " 4)=10/50=1/5 THEORETICAL PROBABILITY What SHOULD happen based on math． Number of ( event )=" favorable outcomes " /■(" Total possible " @" outcomes " ) Example： ROLLING A 4 ON A DIE －Possible outcomes： 1，2，3，4，5， 6 （Total： 6 ） P(" rolling a " 4)=1/6 EXPERIMENTAL PROBABILITY What ACTUALLY happens based on trials． P(" event ")=■(" Number of times " @" event occurs " )/■(" Total number " @" of trials " ) Example： ROLLING A DIE 50 TIMES －Data Collected： Rolling a 4 happened 10 times in 50 trials P(" rolling a " 4)=10/50=1/5 As trials increase Experimental Probability becomes closer to Theoretical Probability AS TRIALS INCREASE... EXPERIMENTAL Probability gets closer to THEORETICAL Probability.