Answer:
(a) The probability that both Dave and Mike will show up is 0.25.
(b) The probability that at least one of them will show up is 0.75.
(c) The probability that neither Dave nor Mike will show up is 0.25.
Step-by-step explanation:
Denote the events as follows:
<em>D</em> = Dave will show up.
<em>M</em> = Mike will show up.
Given:
It is provided that the events of Dave of Mike showing up are independent of each other.
(a)
Compute the probability that both Dave and Mike will show up as follows:
![P(D\cap M)=P(D)\times P (M)\\=[1-P(D^{c})]\times [1-P(M^{c})]\\=[1-0.55]\times[1-0.45]\\=0.2475\\\approx0.25](https://tex.z-dn.net/?f=P%28D%5Ccap%20M%29%3DP%28D%29%5Ctimes%20P%20%28M%29%5C%5C%3D%5B1-P%28D%5E%7Bc%7D%29%5D%5Ctimes%20%5B1-P%28M%5E%7Bc%7D%29%5D%5C%5C%3D%5B1-0.55%5D%5Ctimes%5B1-0.45%5D%5C%5C%3D0.2475%5C%5C%5Capprox0.25)
Thus, the probability that both Dave and Mike will show up is 0.25.
(b)
Compute the probability that at least one of them will show up as follows:
P (At least one of them will show up) = 1 - P (Neither will show up)
![=1-P(D^{c}\cup M^{c})\\=P(D\cup M)\\=P(D)+P(M)-P(D\cap M)\\=[1-P(D^{c})]+[1-P(M^{c})]-P(D\cap M)\\=[1-0.55]+[1-0.45]-0.25\\=0.75](https://tex.z-dn.net/?f=%3D1-P%28D%5E%7Bc%7D%5Ccup%20M%5E%7Bc%7D%29%5C%5C%3DP%28D%5Ccup%20M%29%5C%5C%3DP%28D%29%2BP%28M%29-P%28D%5Ccap%20M%29%5C%5C%3D%5B1-P%28D%5E%7Bc%7D%29%5D%2B%5B1-P%28M%5E%7Bc%7D%29%5D-P%28D%5Ccap%20M%29%5C%5C%3D%5B1-0.55%5D%2B%5B1-0.45%5D-0.25%5C%5C%3D0.75)
Thus, the probability that at least one of them will show up is 0.75.
(c)
Compute the probability that neither Dave nor Mike will show up as follows:
![P(D^{c}\cup M^{c})=1-P(D\cup M)\\=1-P(D)-P(M)+P(D\cap M)\\=1-[1-P(D^{c})]-[1-P(M^{c})]+P(D\cap M)\\=1-[1-0.55]-[1-0.45]+0.25\\=0.25](https://tex.z-dn.net/?f=P%28D%5E%7Bc%7D%5Ccup%20M%5E%7Bc%7D%29%3D1-P%28D%5Ccup%20M%29%5C%5C%3D1-P%28D%29-P%28M%29%2BP%28D%5Ccap%20M%29%5C%5C%3D1-%5B1-P%28D%5E%7Bc%7D%29%5D-%5B1-P%28M%5E%7Bc%7D%29%5D%2BP%28D%5Ccap%20M%29%5C%5C%3D1-%5B1-0.55%5D-%5B1-0.45%5D%2B0.25%5C%5C%3D0.25)
Thus, the probability that neither Dave nor Mike will show up is 0.25.
Answer:
![\sqrt[4]{\frac{5}{7} }](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B%5Cfrac%7B5%7D%7B7%7D%20%7D)
Step-by-step explanation:
^4√5/^4√7
~Apply radical rules
^4√5/7
Best of Luck!
Answer:
that is a negative slope
but dont know how to find the slope sorry
Step-by-step explanation:
Find the median of each set:-
Median is middle number of a data set. If a data set has an odd number of numbers then the median is the middle number when ordered form least to greatest but if its an even number you have to find the mean for the middle 2 numbers when ordered for least to greatest.
A.
1.2, 2.4, 3.2, 3.2, 3.6, 4.0, 4.1, 4.7
Even numbers = 8
3.2 + 3.6 = 6.8
6.8 ÷ 2 =
Median = 3.4
So this shows that A isn't the answer because the median of A is 3.4, not 3.2.
B.
1.6, 2.8, 2.9, 3.1, 3.3, 3.6, 4.2, 4.5
Even numbers = 8
3.1 + 3.3 = 6.4
6.4 ÷ 2 = 3.2
Median = 3.2
<span>So this shows that B is the answer because the median of B is 3.2.
C.
1.8, 2.0, 2.0, 2.2, 3.2, 4.7, 4.8, 4.9
</span>
Even numbers = 8
2.2 + 3.2 = 5.4
5.4 ÷ 2 = 2.7
Median = 2.7
<span>So this shows that C isn't the answer because the median of C is 2.7, not 3.2.
</span>
D.
1.4, 1.7, 2.9, 3.0, 3.1, 3.2, 3.2, 3.2, 4
Odd numbers = 9
Median = 3.1
<span>So this shows that D isn't the answer because the median of D is 3.1, not 3.2.
</span>
The stem and leaf plot which median is 3.2 is B.
