Answer:
a. ![Probability = 0.97735](https://tex.z-dn.net/?f=Probability%20%3D%200.97735)
b. ![Probability = 0.92294](https://tex.z-dn.net/?f=Probability%20%3D%200.92294)
c.
No, it is not unusual if at least 1 lives up to 3.
Step-by-step explanation:
Given
Represent the probability that a 2 year old snake will live to 3 with P(Live);
![P(Live) = 0.98861](https://tex.z-dn.net/?f=P%28Live%29%20%3D%200.98861)
Solving (a): Probability that two selected will live to 3 years.
Both snakes have a chance of 0.98861 to live up to 3 years.
So, the required probability is:
![Probability = P(Live)\ and\ P(Live)](https://tex.z-dn.net/?f=Probability%20%3D%20P%28Live%29%5C%20and%5C%20P%28Live%29)
![Probability = 0.98861 * 0.98861](https://tex.z-dn.net/?f=Probability%20%3D%200.98861%20%2A%200.98861)
![Probability = 0.9773497321](https://tex.z-dn.net/?f=Probability%20%3D%200.9773497321)
<em>--- Approximated</em>
Solving (b): Probability that seven selected will live to 3 years.
All 7 snakes have a chance of 0.98861 to live up to 3 years.
So, the required probability is:
![Probability = P(Live)^n](https://tex.z-dn.net/?f=Probability%20%3D%20P%28Live%29%5En)
Where ![n = 7](https://tex.z-dn.net/?f=n%20%3D%207)
![Probability = 0.98861^7](https://tex.z-dn.net/?f=Probability%20%3D%200.98861%5E7)
![Probability = 0.92294324145](https://tex.z-dn.net/?f=Probability%20%3D%200.92294324145)
<em>--- Approximated</em>
Solving (c): Probability that at least one of seven selected will not live to 3 years.
In probabilities, the following relationship exist:
![P(At\ Least\ One) = 1 - P(None).](https://tex.z-dn.net/?f=P%28At%5C%20Least%5C%20One%29%20%3D%201%20-%20P%28None%29.)
So, first we need to calculate the probability that none of the 7 lived up to 3.
If the probability that one lived up to 3 years is 0.98861, then the probability than one do not live up to 3 years is 1 - 0.98861
This gives:
![P(Not\ Live) = 0.01139](https://tex.z-dn.net/?f=P%28Not%5C%20Live%29%20%3D%200.01139)
The probability that none of the 7 lives up to 3 is:
![P(None) = P(Not\ Live)^7](https://tex.z-dn.net/?f=P%28None%29%20%3D%20P%28Not%5C%20Live%29%5E7)
![P(None) = 0.01139^7](https://tex.z-dn.net/?f=P%28None%29%20%3D%200.01139%5E7)
Substitute this value for P(None) in
![P(At\ Least\ One) = 1 - P(None).](https://tex.z-dn.net/?f=P%28At%5C%20Least%5C%20One%29%20%3D%201%20-%20P%28None%29.)
![P(At\ Least\ One) = 1 - 0.01139^7](https://tex.z-dn.net/?f=P%28At%5C%20Least%5C%20One%29%20%3D%201%20-%200.01139%5E7)
![P(At\ Least\ One) = 0.99999999999997513055642436060443621](https://tex.z-dn.net/?f=P%28At%5C%20Least%5C%20One%29%20%3D%200.99999999999997513055642436060443621)
---- Approximated
No, it is not unusual if at least 1 lives up to 3.
This is so because the above results, which is 1 shows that it is very likely for at least one of the seven to live up to 3 years