(a) The probability that there is no open route from A to B is (0.2)^3 = 0.008.
Therefore the probability that at least one route is open from A to B is given by: 1 - 0.008 = 0.992.
The probability that there is no open route from B to C is (0.2)^2 = 0.04.
Therefore the probability that at least one route is open from B to C is given by:
1 - 0.04 = 0.96.
The probability that at least one route is open from A to C is:

(b)
α The probability that at least one route is open from A to B would become 0.9984. The probability in (a) will become:

β The probability that at least one route is open from B to C would become 0.992. The probability in (a) will become:

Gamma: The probability that a highway between A and C will not be blocked in rush hour is 0.8. We need to find the probability that there is at least one route open from A to C using either a route A to B to C, or the route A to C direct. This is found by using the formula:


Therefore building a highway direct from A to C gives the highest probability that there is at least one route open from A to C.
Answer:

Step-by-step explanation:
We are given the following in the question:

Let l be Lyle's height, h be Harry's height and v be Vince's height.
Thus, we can write:

Lyle's Height =

Harry's height =

Putting the value in the equation:

Thus, Vince's height is 3.5 feet.
It is given here that there is 1/3 probability of professional baseball player will get a hit. Hence if at least three hits are gained out of 5 attempts, the calculation goes: 5C3* (1/3)^3*(2/3)^2 + 5C4* (1/3)^4*(2/3)^1 +5C5 *<span>(1/3)^5*(2/3)^0 equal to 0.21. </span>
Let x - hours Carlos drove ; Let y - hours Maria drove
Equation 1: x + y = 4.4
x = 4.4 - y
Equation 2: 55x + 50y = 233
55(4.4 - y) + 50y = 233
242 - 55y + 50y = 233
-5y = 233-242
-5y = -9
y=9/5 or 1.8 hours Maria drove
To find time Carlos drove:
x=4.4 - 1.8
x = 2.6 hours