This is a binomial experiment and you'll use the binomial probability distribution because:
- There are two choices for each birth. Either you get a girl or you get a boy. So there are two outcomes to each trial. This is where the "bi" comes from in "binomial" (bi means 2).
- Each birth is independent of any other birth. The probability of getting a girl is the same for each trial. In this case, the probability is p = 1/2 = 0.5 = 50%
- There are fixed number of trials. In this case, there are 5 births so n = 5 is the number of trials.
Since all of those conditions above are met, this means we have a binomial experiment.
Some textbooks may split up item #2 into two parts, but I chose to place them together since they are similar ideas.
Answer:
i) Probability that both candidates employed are women = 5/14
ii) Probability that the second candidate is a woman = 5/8
iii) Probability that the first candidate is a woman given that second one is a woman = 4/5
Step-by-step explanation:
Let the probability that a man is employed be P(M) = 3/8
Probability that a woman is employed P(W) = 5/8
a) Probability that both candidates employed are women = (5/8) × (4/7) = 5/14
b) Probability that the second candidate is a woman = (probability that first candidate is a man and second candidate is a woman) + (probability that first candidate is a woman & second candidate is a woman)
= (3/8)(5/7) + (5/8)(4/7) = (15/56) + (20/56) = 35/56 = 5/8
c) Probability that the first candidate is a woman given that second one is a woman
Given that the second candidate was a women, means that the first candidate-women was selected among other four women.
Probability = (4/8)/(5/8) = 4/5
Answer:
See attachment for drawing
Step-by-step explanation:
Given
Required
Draw and label the circle
The equation of a circle is:
Where:
So, we have:
<em>See attachment for drawing</em>
1) 3x+y+z=4
2) 2x+2y+3z=3
3) x+3y+2z = 5
1)*2 6x + 2y + 2z = 8
2) 2x + 2y +3z = 3
- __________________
4x - z = 5
2)*3 6x + 6y + 9z = 9
3)*2 2x + 6y + 4z = 10
- __________________
<span>4x+5z =-1
</span>
4x+5z = -1
4x - z =5
- ________
6z = -6
<u>z = -1
</u><u /><u>
</u>If z=-1,
4x -(-1) =5
4x = 5-1
x = 4/4
<u>x=1</u>
3x+y+z=4
3(1)+y+(-1)=4
3+y-1=4
<u>y=2
So z=-1, x=1, y=2</u>
As per the isosceles triangle theorem, if the two base angles are congruent then the legs are also congruent, so we must set the two legs equal to each other:
2z - 15 = 9
Add 15 to both sides:
15 - 15 = 0
15 + 9 = 24
Divide 2 from each side:
2z = 24
2z/2 = z
24/2 = 12
z = 12
Hence, the answer would be D: z = 12