Suppose the animal shelter has 30% black cats and 70% calico cats. On any given

Question

Suppose the animal shelter has 30% black cats and 70% calico cats. On any given day, a black cat will climb a tree will probability 0.025, while a calico cat climbs a tree with probability 0.010. Aoran goes to the shelter and randomly selects a cat to take home. (a) Find the probability that Aoran's cat climbs a tree on day one after bringing it home. (b) Given Aoran's cat climbs a tree on day one, find the probability his cat is black. (c) Given Aoran's cat climbs a tree on both day one and day two, find the probability his cat is black.

Explanation / Answer

a)P(cat climb tree on day one)=P(cat is black and climb tree on day 1)+P(cat is Calico and climb tree on day 1) =0.3*0.025+0.7*0.01=0.0145

b)

P(Cat is black| cat climb tree on day one)

=P(cat is black and climb tree on day 1)/P(cat climb tree on day one)=0.3*0.025/0.0145=0.517241

c)

P(cat climb tree on both days)=P(cat is black and climb tree on both days)+P(cat is Calico and climb tree on both days)=0.3*0.025*0.025+0.7*0.01*0.01=0.000258

hence P(cat is black|climb tree on both days)

=P(cat is black and climb tree on both days)/P(cat climb tree on both days)

=0.3*0.025*0.025/0.000258 =0.728155

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

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