A newborn baby sometimes cries if she has a problem, and sometimes cries for no

Question

A newborn baby sometimes cries if she has a problem, and sometimes cries for no reason. If she is hungry, she has a 70% chance of crying, if she needs a diaper change she has a 50% chance of crying, and if she is neither hungry or in need of a diaper change, she has a 30% chance of crying anyway. At any given time, she has a 20% chance of being hungry, a 15% chance of needing a diaper change and a 65% chance of neither. (Assume that she couldn't be hungry and need a diaper change at the same time.) i) What is the probability, at any given time, that the baby is crying? ii) Her mom hears the baby crying. What is the probability that the baby needs food? What is the probability that she

Explanation / Answer

Let C denote the event that the baby cries. Also let H denote the event that the baby is hungry, D denote the event that the baby needs a diaper change and N denotes the event that the baby is neither hungry nor needs a diaper change.

Clearly from the given data we have

P(C|H) = 0.7, P(C|D) = 0.5, P(C|N) = 0.3

Also P(H) = 0.2, P(D) = 0.15, P(N) = 0.65

i) The probability, at any given time, that the baby is crying is

P(C) = P(C|H)*P(H) + P(C|D)*P(D) + P(C|N)*P(N)

= 0.41

ii) Her mom hears the baby crying. The probability that the baby needs food is

P(H|C) = P(C|H)*P(H) / P(C)

= 0.14/0.41 = 0.34

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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