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Temperature and hatching How is the hatching of water python eggs influenced by the temperature of a snake鈥檚 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

Expert verified

a. The probability that it hatched is 0.7212.

b. Probability for randomly selected hatched egg was not assigned to hot water is0.4186.

Step by step solution

01

Given Information

It is given that:

02

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

Information regarding 187is given in table.

Possible outcomes are 187

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

P(Hot)=Number of favourable outcomesNumber of possible outcomes=104187

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

Hence, P(Hatched and Hot)=Numberof favourableoutcomesNumber of possible outcomes=75187

Using conditional probability

P(HatchedHot)=P(HatchedandHot)P(Hot)=75187104187=751040.7212=72.12%

Hence, 72.12%of eggs assigned to hot water hatched and probability is0.7212

03

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

We know that P(BA)=P(AB)P(A)=P(AandB)P(A)

In table 129/187eggs are hatched.

P(Hatched)=Numberof favourable outcomesNumber of possibleoutcomes=129187

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

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

P(Hatched and not Hot)=Numberof favourableoutcomesNumber of possible outcomes=54187

Using conditional probability:

P(Hatched|notHot)=P(Hatchedandnot Hot)P(Hatched)=54187129187=54129=18430.4186

=41.86%

About role="math" localid="1654797274671" 41.86%of the hatched eggs were not assigned to hot water and probability is0.4186

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