Answer:
A. 21.06%
B. 66.88%
C. 81.56%
Step-by-step explanation:
There are two possible answer for the question asked, yes(more likely to make purchases) or no. The probability for a random adults answer yes to the question is 32% so the probability that the adults answer no is 68%.
(a) exactly two
There is only one case for this question, 2 people say yes and 8 people say no. The calculation for this problem will be:
2P10 * P(yes)^2 * P(no)^8= 10!/2!8!* 32%^2 * 68%^8 = 0.21066= 21.06%
(b) more than two
There are a lot of case for more than two, its easier to find out the negation of the probability which is "two or less". Case that fulfill "two or less" will be: 2 yes and 8 no
1 yes and 9 no
0 yes and 10 no
The calculation for the negation will be:
~P(X)= 0P10 * P(yes)^0 * P(no)^10 + 1P10 * P(yes)^1 * P(no)^9 + 2P10 * P(yes)^2 * P(no)^8 =
10!/0!10!* 32%^0 * 68%^10 + 10!/1!9!* 32%^1 * 68%^9 + 10!/2!8!* 32%^2 * 68%^8
0.02113 + 0.09947 + 0.21066 = 0.33126= 33.12%
Since its the negation, you need to subtract 1 with the negation
P(X)= 1 - ~P(X)
P(X)= 1 - 33.12%= 66.88%
(c) between two and five, inclusive
Same formula as above, but the case is:
2 yes and 8 no
3 yes and 7 no
4 yes and 6 no
5 yes and 5 no
The calculation will be:
2P10 * P(yes)^2 * P(no)^8 + 3P10 * P(yes)^3 * P(no)^7 + 4P10 * P(yes)^4 * P(no)^6 + 5P10 * P(yes)^5 * P(no)^5 =
10!/2!8!* 32%^2 * 68%^8 + 10!/3!7!* 32%^3 * 68%^7 + 10!/4!6!* 32%^4 * 68%^6 + 10!/5!5!* 32%^5 * 68%^5
0.21066 + 0.26435 + 0.21770 + 0.1229= 0.81561= 81.56%
(It makes it much easier to leave the 2 out for now.)
(I multiplied it by 100 because the first 6 is in the hundredths.
&
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crosses out, because
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