Answer: 0.383 and 0.6671
Step-by-step explanation:
Take 22%, that is 0.22 to be probability of success.
That means "1-0.22 = 0.78" is the probability of failure.
When dealing with selection in probability mathematics, the combination equation is used.
Probability of selecting number 'r' as a successful outcome from a given number 'n' is given as
nCr * p^r * q^n-r
Where p is the probability of success= 0.22
q is the probability of failure= 0.78
n is the total number of sample =10
r is the varying outcome of number of success.
For the first question, number of success is asked to be everything more than 2, that is probability of choosing 3,4,5,6,7,8,9,10 people with a successful outcome (adults who will pay more for environmentally friendly product.)
Instead of going through the long process of checking probability of success for choosing 3,4,5,6,7,8,9,10 adults who will pay more, we can simply find the probability of choosing 0,1,2 adults who will pay more and subtract the answer from 1.
By doing this, we first check for probability of choosing 0 adult that will pay More and this is gotten by putting r=0 in our probability Formula. The Formula becomes
=10C0 * 0.22^0 * 0.78^10
=1 *1 * 0.0834= 0.0834
Hence, Probability of Choosing 0 adult that will Pay more is 0.0834
To Check for probability of choosing 1 adult that will pay more becomes
=10C1 * 0.22^1 * 0.78^9
=10 * 0.22 * 0.1069 = 0.2352
Hence, Probability of choosing 1adult that will pay more = 0.2352
To Check for the probability of choosing 2adults that will pay more becomes
=10C2 * 0.22^2 * 0.78^8
=45 * 0.0484 * 0.1370 = 0.2984
Therefore the total sum of choosing 0,1,2 adults that are willing to pay more becomes
= 0.0834+ 0.2352+ 0.2984 = 0.617
So to determine the probability of choosing more than 2 adults, that is, 3,4,5,6,7,8,9,10 adults that are willing to pay more, we subtract 0.617 from 1.
This gives 1-0.617 = 0.383
Hence, probability of choosing more than 2 people that are willing to pay more than 2 = 0.383.
To determine the probability of choosing between two and five people inclusive, we follow the same probability formular but r becomes 2,3,4,5 differently.
For probability of choosing 2 adults, we already calculated it to be 0.2984 earlier.
For probability of choosing 3 adults, it becomes
10C3 * 0.22^3 * 0.78^7
=120* 0.0106 * 0.1757 = 0.2235
For the probability of choosign 4 adults, it becomes
10C4 * 0.22^4 * 0.78^6
= 210 * 0.0023 * 0.2252 = 0.1088
For the probability of choosing 5 adults, it becomes
10C5 * 0.22^5 * 0.78^5
= 252 * 0.0005 * 0.2887 = 0.0364
Hence, the probability of choosing between 2 and 5 adults becomes
0.2984 + 0.2235 + 0.1088 + 0.0364 = 0.6671
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