probability-game of chances
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probability-game of chances
- 2. • Introduction • Easy examples • Real life examples • Binomial distribution • GeoGebra TOPICS THAT HAVE BEEN COVERED
- 3. Introduction • Many events can't be predicted with total certainty. The best we can say is how likely they are to happen, using the idea of probability. • Probability does not tell us exactly what will happen, it is just a guide
- 4. Binomial Distribution • Each trial can result in just two possible outcomes. We call one of these outcomes a success and the other, a failure. The probability of success, denoted by P, is the same on every trial. The trials are independent; that is, the outcome on one trial does not affect the outcome on other trials.
- 7. More complex examples • Rocket take off Success Failure
- 8. Finding Out The Probability Three stage rocket is about to be launched. In order for a successful launch to occur all three stages of the rocket must successfully pass their pre- take off tests. By default, each stage has a 50% chance of success. Success rate{%} – 10.0000000 Successful Launches – 1 Failed Launches- 9 • 94% success is over a long history of rocket development. More recently, launching agencies have refined their designs and processes to achieve really high reliabilities. Atlas II through Atlas V have had only one partial failure in 120 launches since 1991 • 176 failures from 3024 launches = 5.8% failure. Various assumptions made as to what constitutes failure. • Let's take the one partial failure in 120 data and check whether this is statistically significantly lower than the 94% success rate long term. One could apply the right same principles to the different launch vehicle categories on the comparison of orbital failure and launch. • Assuming the true probability of partial failure were p=6%, as in the figure quoted by Russell's comment, the probability of observing one partial failure or fewer in 120 launches is: 1. 2.
- 9. Probability – Metro EMPTY FULLOR
- 10. Finding The Probability • Now lets calculate the total number of seats in Delhi metro. Total seats in one coach are 50 ( 14+14+14+4+4). Average coach in each train are 6(Refer assumption given below). Total seats in one train = 50x 6 this means 300 seats in one metro. And total of 600000 (300x 2000) seats available in Delhi metro everyday. • Hence now we will talk about the probability of getting a seat in Delhi metro. With total number of ridership of 2.4 million and 6,00,000 seats available we can draw the conclusion that 1 out of 5 people get a seat in Delhi metro(2,400,000/ 600,000). • Hence number of people who travel sitting in metro are 600,000 and those who travel standing are 1,800,000. • This calculation gives a very general result of the possibility of getting a seat. Result may vary according to the time of travel and the line travelled on. ASSUMPTION: The average number of coaches in metro can be taken as 6, we have 4 and 8 coach metro, hence in this case the excess number of coaches in 8 car metro will be compensating for the number of coaches in 4 car metro.
- 11. A digital way of thinking……..solving & understanding