Answer:
Question 4
a) 0.667
b) 0.833
c) 0.833
d) 0
Question 5
a) 32 yards
b) $312
Explanation:
Probability question 4
The best way to solve these probability questions is to enumerate and count the total set of outcomes and then enumerate and count the specific set of outcomes they are looking for in each part .
Since the experiment consists of rolling a fair single 6-sided die we can enumerate the set of possible outcomes as
{1, 2, 3, 4, 5, 6}. This is also referred to in probability as sample space.
There are 6 possible outcomes
The probability of getting any one number is 1/6 whether it be a 1, a 2 or 3, 4, 5 or 6.
In general P(a specific outcome) = Number of ways of getting that outcome ÷ total number of all possible outcomes
part a)
Rolling an even==> Set of outcomes = {2, 4, 6}
Rolling a 3 => {3}
Rolling a 3 or even = {2, 3, 4, 6}; 4 elements
P(even or 3 ) = 4/6 = 2/3 = 0.667
Part b)
Number > 2 ==> { 3, 4, 5, 6}
Even: {2, 4, 6}
Even or greater than 2 = {2, 3, 4, 5, 6}; 5 elements - we do not duplicate
P(Even or greater than 2 ) = 5/6 = 0.833
part c)
Odd number: {1, 3, 5}
Number less than 6: {1, 2, 3, 4, 5}
Combining the two we get: {1, 2, 3, 4, 5} for a total of 5 outcomes
P(odd or less-than 6 ) = 5/6 = 0.833
part(d)
Rolling a 2 and a 4
You cannot roll a 2 and a 4 in one toss so the probability is 0
Question 5
I think you have overly complicated the working of this problem. There is no need to use right triangle, hypotenuse etc
If you have a rectangle with length = L and width = W, the perimeter is just
P = 2( L + W)
Here we can choose any dimension for L and the other for W
Let's choose L = 11 (greater number)
W = 5
Perimeter P = 2 (11 + 5) = 2(16) = 32 yards
b) It costs $3.25 per foot for the fencing..
Careful! The only tricky part here is the units. It is given in $ per square foot whereas the dimensions of the plot are given in yards and the perimeter is also in yards. Watch out for these tricks in other questions
Convert perimeter from yards to feet
32 yards = 32 x 3 = 96 feet (there are 3 feet to a yard)
Cost of 96 feet of fencing at $3.25 per foot
= 96 x 3.25 = $312