Map Sapling Learning macmillan learning this question was written by Jeremy Schm

Question

Map Sapling Learning macmillan learning this question was written by Jeremy Schmit at Kansas State University Consider a series of 8 flips of a fair coin Calculate the probabilities for obtaining 0-8 heads. We will consider each of these nine outcomes to be macrostates of the system. Graph these probabilities below. Please select the "point" option on the graphing tool to graph the probabilities. 0 0.35 0.30 0.25 Probability 0.20 0.15 0.10 0.05 Incorrect. 0.00 0 6 Number of heads e Previous Give Up & View Solution Try Again Next Exit about us careersprivacy policy tems of use contact us help

Explanation / Answer

The probaility can be determined using binomial distribution. For r heads in n trials ,the probability is given by

P(r) = nCr(1-0.5)n-r0.5r

Probability of 0 head = 8C0*(1-0.5)8 = 1*0.58=0.0039

Probability of one head = 8C1(1-0.5)(1-0.5)7=0.03125

Probability of 2 heads = 8C2(1-0.5)2(1-0.5)6=0.109

Probability of 3 heads =  8C3(1-0.5)3(1-0.5)5=0.219

Probability of 4 heads =  8C4(1-0.5)4(1-0.5)4=0.273

Probability of 5 heads =  8C5(1-0.5)5(1-0.5)3=0.219

Probability of 6 heads =  8C6(1-0.5)2(1-0.5)+=0.109

Probability of 7 heads =  8C7(1-0.5)7(1-0.5)1=0.03125

Probability of 8 heads= 8C8(1-0.5)0(1-0.5)8=0.0039

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.