Consider a game where you throw balls at a (virtual) object. Each time you throw

Question

Consider a game where you throw balls at a (virtual) object. Each time you throw the ball, you have a 1/16 chance of success at capturing the object. (a) If you have 9 balls to throw, what is the probability that you capture the object? (you capture the object if at least one throw is successful) (b) Assume that one "game" allows you to throw k balls, and that the probability of a successful game (the object is captured) is 0.36. What is the expected number of games that you would need to play in order to have a successful game? (c) Using the same scenario as for (b), what is the expected number of successful games if you play 14 games?

Explanation / Answer

(a) Probability that a throw is successful = 1/16

=> Probability that a throw is not successful = 15/16

Probability that 9 throws are unsuccessful = (15/16)9

=> Probability that atleast one throw is successful = 1 - (15/16)9

= 0.44

(b) Using the logic above we have

After k throws, probability that atleast one throw is successful = 1 - (15/16)k = 0.36

=> (15/16)k = 1 - 0.36 = 0.64

=> 0.9375k = 0.64

=> k = log 0.64 / log 0.9375

=> k = 6.915

Therefore, the expected number of games is 7.

(c) Since 7 games gives a success, the expected number of successful games after 14 games = 14/7 = 2.

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

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