5.2.4 case 1 binomial probability distribution
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This document discusses the binomial probability distribution and provides examples of calculating probabilities of coin toss outcomes. Specifically, it addresses: 1) Calculating the probability of getting exactly 5 heads, at least 8 heads, not more than 3 heads, and at least one head when tossing 10 coins. 2) If the 10 coin toss is repeated 50 times, calculating the expected number of times exactly 5 heads will occur. 3) Explaining the case of the binomial probability distribution and providing contact information for the presenter.
5.2.4 case 1 binomial probability distribution
- 1. www.sanjivanimba.org.in Unit No.5. PROBABILITY DISTRIBUTION Presented By: Dr. V. M. Tidake Ph. D (Financial Management), MBA(FM), MBA(HRM) BE(Chem) Dean, EDP & Associate Professor MBA 1 Sanjivani College of Engineering, Kopargaon Department of MBA www.sanjivanimba.org.in
- 2. www.sanjivanimba.org.in 302-DECISION SCIENCE Unit No.5. Probability 5.2.4 Case 1: Binomial Probability Distribution Presented By: Dr. V. M. Tidake Ph. D (Financial Management), MBA(FM), MBA(HRM) BE(Chem) Dean EDP & Associate Professor MBA 2 Sanjivani College of Engineering, Kopargaon Department of MBA www.sanjivanimba.org.in
- 3. www.sanjivanimba.org.in NETWORK ANALYSIS At the End of the Session Student will be able to understand- A. Case 1: Binomial Probability Distribution
- 4. www.sanjivanimba.org.in Probability Distribution 10 Unbiased coins are tossed simultaneously, find the probability that there will be- i. Exactly 5 heads ii. At least 8 heads iii. Not more than 3 heads iv. At least one head v. If this exercise is carried out 50 times, how many times we can get exactly 5 heads?
- 5. www.sanjivanimba.org.in Case 1: Binomial Distribution Let, p - Probability of getting Head = ½ Similarly, q - Probability of getting Tail = ½ Also the experience is performed using 10 coins i.e. it is carried out n = 10 number of times. Hence the probability of getting r successes in 10 trials is given by Binomial Probability Function as- P(r) = 10Crprq10-r = 10Cr ( 𝟏 𝟐 )r ( 𝟏 𝟐 )10-r = 10Cr ( 𝟏 𝟐 )10 = 𝟏 𝟏𝟎𝟐𝟒 10Cr
- 6. www.sanjivanimba.org.in Case 1: Binomial Distribution i. Probability of getting 5 heads i.e. r = 5 is- P(5) = 𝟏 𝟏𝟎𝟐𝟒 10C5 P(5) = 𝟏 𝟏𝟎𝟐𝟒 ∗ 𝟏𝟎∗𝟗∗𝟖∗𝟕∗𝟔 𝟏∗𝟐∗𝟑∗𝟒∗𝟓 P(5) = 𝟎. 𝟐𝟒𝟔
- 7. www.sanjivanimba.org.in Case 1: Binomial Distribution ii. Probability of getting at least 8 heads i.e. r ≥ 8 is- P(r ≥ 8) = P r = 8 or 9 or 10 = P 8 + P 9 + P 10 P(r ≥ 8) = 1 1024 (10C8 + 10C9 +10C10) P(r ≥ 8) = 1 1024 (10C2 + 10C1 +10C0) P(r ≥ 8) = 1 1024 ∗ 10∗9 1∗2 + 10 + 1 P(r ≥ 8) = 1 1024 ∗ 56 P(r ≥ 8) = 0.055
- 8. www.sanjivanimba.org.in Case 1: Binomial Distribution iii. Probability of not more than 3 heads i.e. r ≤ 3 is- P(r ≤ 3) = P r = 0 or 1 or 2 or 3 = P 0 + P 1 + P 2 + P 3 P(r ≤ 3) = 1 1024 (10C0 + 10C1 +10C2 + 10C3) P(r ≤ 3) = 1 1024 ∗ 1 + 10 + 10∗9 1∗2 + 10∗9∗8 1∗2∗3 P(r ≤ 3) = 1 1024 ∗ 1 + 10 + 45 + 120 = 176 1024 P(r ≤ 3) = 0.172
- 9. www.sanjivanimba.org.in Case 1: Binomial Distribution iv. At least 1 head i.e. r ≥ 1 is- P(r ≥ 1) = 1 − P r ˂ 1 = 1 − P 0 P(r ≥ 1) = 1 - 1 1024 (10C0) P(r ≥ 1) = 1 - 1 1024 P(r ≥ 1) = 1023 1024 P(r ≥ 1) = 0.9
- 10. www.sanjivanimba.org.in Case 1: Binomial Distribution v. Possibility of getting 5 Heads: If the exercise of throwing n=10 coins is repeated for N=50 Times, Then the number of times we expect to get 5 heads is- = f(5) = N * P(5) = 50 * 0.246 =12.3 i.e. 12
- 11. www.sanjivanimba.org.in EXERCISE Explain case 1: Binomial Probability Distribution
- 12. www.sanjivanimba.org.in For More Details Contact Dr. V M Tidake tidkevishal@gmail.com tidkevishalmba@sanjivani.org.in