An article in the The Canadian Entomologist reported on the life of the alfalfa

Question

An article in the The Canadian Entomologist reported on the life of the alfalfa weevil from eggs to adulthood. The following table shows the number of larvae that survived at each stage of development from eggs to adults. What is the probability an egg survives to adulthood? What is the probability of survival to adulthood given survival to the late larvae stage? What stage has the lowest probability of survival to the next stage? Bonus! What is the probability of larvae cannot survive to late larvae given it survived at early larvae?

Explanation / Answer

Let A be the event that egg survives to adulthood.

EL be the event that an egg survives at early larvae stage.

LL be the event that an egg survuves at late larve stage.

PP be the event that an egg survives at Pre-pupae stage.

LP be the event that an egg survives at late Pupae stage.

1. P(A) = number of egg survives to adulthood / number of eggs = 31/421 = 0.0736

2. P(A/LL) = P(A and LL) / P(LL)

P(A and LL) =number of egg survives to adulthood and late larvae / no. of eggs

P(A and LL) = 31/421 = 0.0736

P(LL) = number of egg survives to late larvae / no. of eggs

= 306 / 421 = 0.7278

P(A/LL) = P(A and LL) / P(LL)

= 0.0736 / 0.7268 = 0.1013

c) P(EL) = number of egg survives to early larvae late larvae / no. of eggs

= 412 / 421 = 0.9786

P(LL/EL) = P(LL and EL) / P(EL)

P(LL and EL) = number of egg survives to late larvae early larvae / no. of eggs

= 306/421 = 0.7268

P(EL) = number of egg survives to early larvae / no. of eggs

= 412 / 421 = 0.9786

P(LL/EL) = 0.7268 / 0.9786 = 0.7427

P(PP/LL) = P(PP and LL) / P(LL)

P(PP and LL) = number of egg survives to pre pupae and late larvae / no. of eggs

= 45 / 421 = 0.1069

P(LL) = number of egg survives to late larvae / no. of eggs

= 306/421 = 0.7268

P(PP/LL) = 0.1069 / 0.7268 = 0.1471

P(LP/PP) = P(LP and PP) / P(PP)

P(LP and PP) = number of egg survives to late larvae and pre pupae / no. of eggs

= 35 / 421 = 0.0831

P(PP) = number of egg survives to prepupae / no. of eggs

= 45 / 421 = 0.1069

P(LP/PP) / P(PP) = 0.0831 / 0.1069 = 0.7777

P(A / LP) = P(A and LP) / P(LP)

P(A and LP) = number of egg survives to adulthood and late pupae / no. of eggs

= 31/ 421 = 0.0736

P(LP) = 35 / 421 = 0.0831

P(A and LP) = 0.0736 / 0.0831 = 0.8857

The late larvae stage has the lowest probability of survival to the pre-pupae stage.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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