   Chapter 14.3, Problem 27E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# Germination Rates A certain brand of tomato seeds has a 0.75 probability of germinating. To increase the chance that at least one tomato plant per seed hill germinates, a gardener plants four seeds in each bill.(a) What is the probability that at least one seed germinates in a given hill?(b) What is the probability that two or more seeds will germinate in a given hill?(c) What is the probability that all four seeds germinate in a given hill?

To determine

(a)

To find:

The probability that at least one seed germinates in a given hill.

Explanation

Given:

A certain brand of tomato seeds has a 0.75 probability of germinating. To increase the chance that at least one tomato plant per seed hill germinates, a gardener plants four seeds in each bill.

Approach:

The formula for getting exactly r successes in n independent trials is

P(X=r)=C(n,r)pr(1p)nr(1)

Here, X is a random variable.

The formula for the complement of event E is P(E)=1P(E)(2)

Here, E denotes the complement of E.

Calculation:

Let X be the event that seeds germinate.

From the given information, p=0.75, n=4.

P(X1)=1P(X<1)=1P(X=0)

Substitute 0

To determine

(b)

To find:

The probability that two or more seeds will germinate.

To determine

(c)

To find:

The probability that all seeds will germinate.

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