The probability for part (a) is 0.131, for part (b) is 0.795, for part (c) is 0.0733.
It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
41% of adults say cashews are their favorite kind of nut.
P = 41% = 0.41
Q = 1 - P = 1 - 0.41 = 0.59
n = 2
From the binomial distribution:
[tex]\rm P(X = r) = C(n, r) P^r(1-P)^{n-r}[/tex]
a) Exactly​ three
[tex]P(X=3) = C(12, 3) (0.41)^3(0.59)^9[/tex]
P(X = 3) = 0.131
b) At least​ four:
P(X≥4) = P(X=4)+ P(X=5)+ P(X=6)+..............+ P(X=13)
[tex]\rm P(X\geq 4)=C(12, 4) (0.41)^4(0.59)^9+C(12, 5) (0.41)^5(0.59)^8+...............+C(12, 3)(0.41)^3(0.59)^9[/tex]
P(X ≥ 4) = 0.795
c) At most two:
P(X≤2) =P(X=0)+ P(X=1)+ P(X=2)
[tex]\rm =C(12, 0) (0.41)^0(0.59)^12+C(12, 1) (0.41)^1(0.59)^1^1+C(12, 2)(0.41)^2(0.59)^1^0[/tex]
P(X ≤ 2) = 0.0733
Thus, the probability for part (a) is 0.131, for part (b) is 0.795, for part (c) is 0.0733.
Learn more about the probability here:
brainly.com/question/11234923
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