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Some probability problems follow a special pattern.
If a scenario meets the four conditions, then we call it a BINOMIAL problem
B(Binary
I(Independent Trials
N(Number of trials is fixed
S(Success probability constant)
1) Binary — (does it have two outcomes)
— one called a “success” and the other a “failure:
EX: have a baby boy vs baby girl
correct answer vs incorrect answer
Make a FT vs miss a FT
select a red M&M vs not a red M&M
2) Independent trials
— the result of one trial should have no impact on future trials
EX: u have 3 kids
10 multiple choice questions
20 FT attempt
40 M&M’s in a bag
3) Fixed number of trials
— we are going to carry out a repeated procedure only so many times
4) The probability of success constant
— the success probability should NOT change from one trial to the next trial
EX: baby boy vs baby girl (50/50)
10 multiple choice Q’s [5 choices] (80/20)
20 FT attempts (?/?)
40 M&M’s in a bag (1/6 to 5/6)
EXAMPLE!!!
1) Binary — yes! either red or black card
2) Independent — no… bc each card is discarded meaning that it will affect the next chance that someone guesses a black/red card (one card less)
3) Number of trials fixed — process is repeated 10 times
4) Sucess probability — no bc of the cards being discarded
another example! Roll a fie 3 times and let X = the number of 4’s
1) B — YES! there’s two outcomes (either 4 or not a 4)
2) I — YES!
3) N — YES! we’re rolling 3 times
4) S— 1/6 chance of seeing a 4.. so yes there’s success
If a scenario has two outcomes, independent trials, a constant probability of success, BUT you are interested in the number of trials until the FIRST success, then we have a GEOMETRIC DISTRIBUTION
yur
