Answer:
[tex]Probability = 0.9921[/tex]
Step-by-step explanation:
Given
Represent the proportion of unlicensed stray dog with p
[tex]P = 2\%[/tex]
[tex]n = 7[/tex]
Convert p to decimal
[tex]p = 0.02[/tex]
First we need to determine the proportion of licensed stray dogs.
Represent this with q
In probability,
[tex]p + q = 1[/tex]
Solve for q
[tex]q = 1 - p[/tex]
[tex]q = 1 - 0.02[/tex]
[tex]q = 0.98[/tex]
The probabiliy is binomial and it is represented as thus:
[tex](p + q)^n = ^nC_0p^0q^{n-0} + ^nC_1p^1q^{n-1} + ^nC_2p^2q^{n-2} + .... + ^nC_np^nq^{0}[/tex]
Since we have that fewer than two is selected.
[tex]Probability = ^nC_0p^0q^{n-0} + ^nC_1p^1q^{n-1}[/tex]
Substitute values for p, q and n
[tex]Probability = ^7C_0 * 0.02^0 * 0.98^{7-0} + ^7C_1 * 0.02^1 * 0.98^{7-1}[/tex]
[tex]Probability = 1 * 1 * 0.98^7 + 7 * 0.02 * 0.98^6[/tex]
[tex]Probability = 0.86812553324 + 0.12401793332[/tex]
[tex]Probability = 0.99214346656[/tex]
[tex]Probability = 0.9921[/tex] ---Approximated
