A biologist is collecting insects in a field. Beetles represent 67 percent of all the insects that have been collected so far. What is the probability that exactly half of the next 6 insects collected will be beetles?

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1. A biologist is collecting insects in a field. Beetles represent 67 percent of all the insects that have been collected so far. What is the probability that exactly half of the next 6 insects collected will be beetles?

0.21617

Solution
(₆C₃)(0.67)³(1-0.67)³
= 0.21617
A = 45.6° , B = 57.6° , C = 76.9°

Solution
Use Law of Cosines

cos A = (b² + c² - a²)/2bc
cos A = (13² + 15² - 11²)/(2 × 13 ×15)
cos A = 7/10
cos⁻¹(7/10) = 45.6°

cos B = (c² + a² - b²)/2ca
cos B = (15² + 11² - 13²)/(2 × 15 × 11)
cos B = 59/110
cos⁻¹(59/110) = 57.6°

cos C = (a² + b² - c²)/2ab
cos C = (11² + 13² - 15²)/(2 × 11 × 13)
cos C = 5/22
cos⁻¹(5/22) = 76.9°
y = 5x/3 + 15
28.8

Solution
∠A + 61° + 76° = 180°
∠A = 43°

Use Law of Sines
a/sin(43°) = 41/sin(76°)
a = 41sin(43°)/sin(76°)
a = 28.8

A biologist is collecting insects in a field. Beetles represent 67 percent of all the insects that have been collected so far. What is the probability that exactly half of the next 6 insects collected will be beetles?

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A biologist is collecting insects in a field. Beetles represent 67 percent of all the insects that have been collected so far. What is the probability that exactly half of the next 6 insects collected will be beetles?

❤ If you liked Fatskills, consider supporting us by checking out The Life Manuals You Never Got.

About | Explore | User Guide | Topics | Subjects | Doubt Solver | Career Aptitude Test | Answers | Free Tools | What Should We Know? Privacy | Terms |

Without work one finishes nothing. - Ralph Waldo Emerson© 2026 Fatskills.com

All trademarks, logos and brand names are the property of their respective owners. All company, product and service names used in this website are for identification purposes only. Use of these names, trademarks and brands does not imply endorsement.

About | Explore | User Guide | Topics | Subjects | Doubt Solver | Career Aptitude Test | Answers | Free Tools | What Should We Know?
Privacy | Terms |

Without work one finishes nothing. - Ralph Waldo Emerson
© 2026 Fatskills.com