Answer:
(a) The probability that two randomly selected 5-year-old male horned beetles will live to be 6 years old is 0.06566.
(b) The probability that six randomly selected 5-year-old male horned beetles will live to be 6 years old is 0.000283.
Step-by-step explanation:
It is given that the probability that a randomly selected 5-year-old male horned beetle will live to be 6 years old is 0.25624.
(a)
We need to find the probability that two randomly selected 5-year-old male horned beetles will live to be 6 years old.
![P=0.25624\times 0.25624=(0.25624)^2=0.0656589376\approx 0.06566](https://tex.z-dn.net/?f=P%3D0.25624%5Ctimes%200.25624%3D%280.25624%29%5E2%3D0.0656589376%5Capprox%200.06566)
Therefore the probability that two randomly selected 5-year-old male horned beetles will live to be 6 years old is 0.06566.
(b)
We need to find the probability that six randomly selected 5-year-old male horned beetles will live to be 6 years old.
![P=0.25624\times 0.25624\times 0.25624\times 0.25624\times 0.25624\times 0.25624=(0.25624)^6=0.000283061988948\approx 0.000283](https://tex.z-dn.net/?f=P%3D0.25624%5Ctimes%200.25624%5Ctimes%200.25624%5Ctimes%200.25624%5Ctimes%200.25624%5Ctimes%200.25624%3D%280.25624%29%5E6%3D0.000283061988948%5Capprox%200.000283)
Therefore the probability that six randomly selected 5-year-old male horned beetles will live to be 6 years old is 0.000283.