Question

Temperature and hatching How is the hatching of water python eggs influenced by the temperature of a snake’s nest? Researchers randomly assigned newly laid eggs to one of three water temperatures: cold, neutral, or hot. Hot duplicates the extra warmth provided by the mother python, and cold duplicates the absence of the mother.

Suppose we select one of the eggs at random.

a. Given that the chosen egg was assigned to hot water, what is the probability that it hatched?

b. If the chosen egg hatched, what is the probability that it was not assigned to hot water?

Short answer

a. The probability that it hatched is $0.7212$.

b. Probability for randomly selected hatched egg was not assigned to hot water is$0.4186$.

Step-by-step solution

Given Information

It is given that:

Probability for the chosen hatched egg was not assigned to hot water.

Information regarding $187$is given in table.

Possible outcomes are $187$

In table, $104/187$eggs are assigned hot water.

$P\left(\mathrm{Hot}\right)=\frac{\text{Number of favourable outcomes}}{\text{Number of possible outcomes}}=\frac{104}{187}$

Also, in table $75/187$are assigned to hot water and hatched.

Hence, $P\left(\text{Hatched and Hot}\right)=\frac{\text{Numberof favourableoutcomes}}{\text{Number of possible outcomes}}=\frac{75}{187}$

Using conditional probability

$P(\text{Hatched}\mid \text{Hot})=\frac{P\left(\text{HatchedandHot}\right)}{P\left(\text{Hot}\right)}=\frac{\frac{75}{187}}{\frac{104}{187}}=\frac{75}{104}\approx 0.7212=72.12\%$

Hence, $72.12\%$of eggs assigned to hot water hatched and probability is$0.7212$

Probability for the chosen hatched egg was not assigned to hot water.

We know that $P(\mathrm{B}\mid \mathrm{A})=\frac{P(\mathrm{A}\cap \mathrm{B})}{P(\mathrm{A})}=\frac{P(\mathrm{A}\text{and}\mathrm{B})}{P(\mathrm{A})}$

In table $129/187$eggs are hatched.

$\Rightarrow P\left(\text{Hatched}\right)=\frac{\text{Numberof favourable outcomes}}{\text{Number of possibleoutcomes}}=\frac{129}{187}$

Also in table, $16$hatched eggs are assigned to cold water and $38$hatched eggs are assigned to neutral water.

role="math" localid="1654797169661" $\Rightarrow 54$hatched eggs are not assigned to hot water.

$P\left(\text{Hatched and not Hot}\right)=\frac{\text{Numberof favourableoutcomes}}{\text{Number of possible outcomes}}=\frac{54}{187}$

Using conditional probability:

$P\left(\text{Hatched|notHot}\right)=\frac{P\left(\text{Hatchedandnot Hot}\right)}{P\left(\text{Hatched}\right)}=\frac{\frac{54}{187}}{\frac{129}{187}}=\frac{54}{129}=\frac{18}{43}\approx 0.4186$

$=41.86\%$

About role="math" localid="1654797274671" $41.86\%$of the hatched eggs were not assigned to hot water and probability is$0.4186$