1) D
2)
3) B
4 ) F
5)C
6) F
7) D
8) C
I'm not sure about questions 4 and 7, but they may be correct.
I couldn't because I couldn't see the 2nd question
Answer:
a) P=0.2503
b) P=0.2759
c) P=0.3874
d) P=0.2051
Step-by-step explanation:
We have this information:
25% of American households have only dogs (one or more dogs)
15% of American households have only cats (one or more cats)
10% of American households have dogs and cats (one or more of each)
50% of American households do not have any dogs or cats.
The sample is n=10
a) Probability that exactly 3 have only dogs (p=0.25)
![P(x=3)=\binom{10}{3}0.25^30.75^7=120*0.01563*0.13348=0.25028](https://tex.z-dn.net/?f=P%28x%3D3%29%3D%5Cbinom%7B10%7D%7B3%7D0.25%5E30.75%5E7%3D120%2A0.01563%2A0.13348%3D0.25028)
b) Probability that exactly 2 has only cats (p=0.15)
![P(x=2)=\binom{10}{2}0.15^20.85^8=45*0.0225*0.27249=0.2759](https://tex.z-dn.net/?f=P%28x%3D2%29%3D%5Cbinom%7B10%7D%7B2%7D0.15%5E20.85%5E8%3D45%2A0.0225%2A0.27249%3D0.2759)
c) Probability that exactly 1 has cats and dogs (p=0.1)
![P(x=1)=\binom{10}{1}0.10^10.90^0=10*0.1*0.38742=0.38742](https://tex.z-dn.net/?f=P%28x%3D1%29%3D%5Cbinom%7B10%7D%7B1%7D0.10%5E10.90%5E0%3D10%2A0.1%2A0.38742%3D0.38742)
d) Probability that exactly 4 has neither cats or dogs (p=0.5)
![P(x=4)=\binom{10}{4}0.50^40.50^6=210*0.0625*0.01563=0.20508](https://tex.z-dn.net/?f=P%28x%3D4%29%3D%5Cbinom%7B10%7D%7B4%7D0.50%5E40.50%5E6%3D210%2A0.0625%2A0.01563%3D0.20508)