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Challenging problems on Binomial distribution probability
Problem 1Let X represents the difference between the number of heads and the number of tails
when a coin is tossed 33 times. Find P (X=3).
Solution
In this problem, the sum Heads+Tails is 33, while the difference Heads-Tails = 3.
It immediately implies that Heads = 18, Tails = 15.
Therefore, the event X= 3 is EQUIVALENT to event Tails = 15.
Now, P(Tails=15) is (use the formula of probability for the Binomial distribution)
P(Tails=15) = = BIMON.DIST(15, 33, 0.5, FALSE) = 0.120741. ANSWER
I used the standard EXCEL function to calculate the binomial distribution probability.
Its first parameter is the "number of successful trials" (k= 15 in this case).
Its second parameter is the "number of trials n" (n= 33 in this case).
Its third parameter is "the probability of success in each one single trial" (p= 0.5 in this case); and
The fourth parameter says if you want calculate a single addend or the sum of addends (the single addend in this case).
Input "=BINOM.DIST(15, 33, 0.5, FALSE)" into any MS Excel cell in your computer and press enter to get the answer P = 0.120741 immediately.
On Excel function BINOM.DIST, see its description everywhere, for example
https://support.office.com/en-us/article/binom-dist-function-c5ae37b6-f39c-4be2-94c2-509a1480770c
Problem 2A person flips a coin to determine whether she's moving forwards or backward.
If she flips a head, she moves 1 step forward, and if she flips a tail, she moves 1 step backward.
What is the probability that after 4 coin tosses, she will be in the same place?
Solution
It is the probability of getting two tails and two heads of 4 flips in any order
P(2T2H of 4) = = = 0.375. ANSWER
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- How to calculate Binomial probabilities with Technology (using MS Excel)
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Use this file/link ALGEBRA-II - YOUR ONLINE TEXTBOOK to navigate over all topics and lessons of the online textbook ALGEBRA-II.
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