Answer:
1) 0.3456
2) 0.6544.
Step-by-step explanation:
Let X represents the event of recognizing the brand,
Given,
The probability of recognizing the brand, p = 40% = 0.40,
Thus, the probability of not recognizing the brand, q = 1 - 0.40 = 0.60,
Since, the binomial distribution formula,
[tex]P(x) = ^nC_r (p)^r(q)^{n-r}[/tex]
Where,
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
1) Thus, the probability that exactly 2 of the 5 consumers recognize the brand name is,
[tex]P(X=2)=^5C_2 (0.40)^2 (0.60)^{5-2}[/tex]
[tex]=10 (0.40)^2 (0.60)^3[/tex]
[tex]=0.3456[/tex]
2) Also, the probability that the number who recognize the brand name is not 2 = 1 - P(X=2) = 1 - 0.3456 = 0.6544.
