Suppose Jane has a fair 3-sided die, and Dick has a fair 8-sided die. Each day,

Question

Suppose Jane has a fair 3-sided die, and Dick has a fair 8-sided die. Each day, they roll their dice (independently) until someone rolls a "1". (Then the person who did not roll a "1" does the dishes.) Find the probability that 1. they roll the first "1" at the same time (after equal number of attempts); 1/9 Submit Answer Incorrect. Tries 1/5 Previous Tries 2. it takes Dick twice as many attempts as it does Jane to roll the first "1 You are correct. r receipt no. is 154-9043Previous Tries 3. Dick rolls the first "1" before Jane does. 1/3 Submit Answer Incorrect. Tries 2/5 Previous Tries

Explanation / Answer

1.To get both 1s at the same time, Jane and Dik both have to get 1. Prob(Jane getting 1)=1/3 and Prob(Dik getting a 1)=1/8, Thus Prob(Jane and Dik get a 1)=1/3*1/8=1/24 after any number of equal attempts. But the attempts may be 1,2...infinity. Thus Total probability is =1/24+2/3*7/8*1/24(after 2attempts)+(14/24)^2*1/24+...

Thus total probability= 1/24*(1+14/24+(14/24)^2+(14/24)^3+....)=1/24*24/10=1/10(answer)

3. Dik rolls the first 1 befor Jane. Then total cases would Dik rolls 1 in first attempt(Jane hasn't)+Dik rolls 1 in second attempt(Jane doesn't)+....infinity. Prob(Jane doesnt roll 1)=2/3. Prob(Dik rolls 1)=1/8 and Prob(Dik doesnt roll 1)=7/8. Thus total probability= 2/3*1/8+(2/3)^2*7/8*1/8+(2/3)^3*(7/8)^2*1/8+....=1/8*2/3*[1+14/24+(14/24)^2+....infinity]=2/24*24/10=2/10=1/5(answer).

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

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