Respuesta :
[tex] {\text{Total number of woolen overcoat = 15}} \hfill \\
{\text{Number of ladies in a group = 6}} \hfill \\
{\text{Each lady has 15 choices, which can happen in = 1}}{{\text{5}}^6}{\text{ ways}} \hfill \\
{\text{If no two ladies have the same choices, then each lady can select any overcoat}}. \hfill \\
{\text{Six ladies can select the woolen overcoat in = 15}} \times {\text{14}} \times {\text{13}} \times {\text{12}} \times {\text{11}} \times {\text{10 ways}} \hfill \\ [/tex][tex] \therefore \,{\text{The probability that no two ladies select the same overcoat = }}P\left( E \right){\text{ = }}\frac{{{\text{15}} \times {\text{14}} \times {\text{13}} \times {\text{12}} \times {\text{11}} \times {\text{10 }}}}{{{\text{1}}{{\text{5}}^6}}}\; \hfill \\
\therefore \,{\text{The probability that atleast two ladies select the same overcoat }} \hfill \\
\,\,\,{\text{ = }}\,{\text{1}} - P\left( E \right) \hfill \\ [/tex][tex] \,\,\,{\text{ = }}\,{\text{1}} - \frac{{{\text{15}} \times {\text{14}} \times {\text{13}} \times {\text{12}} \times {\text{11}} \times {\text{10 }}}}{{{\text{15}} \times {\text{15}} \times {{15}^4}}}\hfill \\
\,\,\,{\text{ = }}\,{\text{1}} - \frac{{{\text{14}} \times {\text{13}} \times {\text{4}} \times {\text{11}} \times {\text{2 }}}}{{{{15}^4}}} \hfill \\
\,\,\,{\text{ = }}\,{\text{1}} - \frac{{{\text{16016 }}}}{{{\text{50625}}}} \hfill \\ [/tex][tex] \,\,\,{\text{ = }}\,{\text{1}} - {\text{0}}{\text{.316}} \hfill \\
\,\,\,{\text{ = }}\,0.684 \hfill \\ [/tex]
The probability that at least 2 ladies choose the same type of overcoat will be 0.32.
What is probability?
Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
Each of the 6 ladies randomly chooses a woolen overcoat from 15 different styles.
Then the probability that at least 2 ladies choose the same type of overcoat will be
The total number of the event will be
Total events = 15⁶
The favorable event will be
Favorable event = 15 x 14 x 13 x 12 x 11 x 10
Then the probability will be
P = (15 x 14 x 13 x 12 x 11 x 10) / 15⁶
P = 0.31636
P = 0.32
More about the probability link is given below.
https://brainly.com/question/795909
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