Probability Game of chance Binomial distribution Throwing of a dice Cell phone transmission Earthquakes Metro

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.

5. Examples(easy)

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