Question

 There are 7 Democrats and 6 Republicans on a local city council. A planning committee of 6 for affordable housing needs to be created. Find the probability that the group is made up of at least 4 Democrats.

Answer 1

Answer:

The probability is $0.383$.

Step-by-step explanation:

There are 7 democrats and 6 republicans  

Number of ways in which 4 democrats and 2 republicans can be selected=$\[{}^{7}{{C}_{4}}\times {}^{6}{{C}_{2}}\]$

Number of ways in which 5 democrats and 1 republican can be selected= $\[{}^{7}{{C}_{5}}\times {}^{6}{{C}_{1}}\]$

Number of ways in which 6 democrats can be selected = $\[{}^{7}{{C}_{6}}\]$

So, favourable outcomes are $\[{}^{7}{{C}_{4}}\times {}^{6}{{C}_{2}}+{}^{7}{{C}_{5}}\times {}^{6}{{C}_{1}}+{}^{7}{{C}_{6}}\]$

Total possible outcomes =$\[{}^{13}{{C}_{6}}\]$

Now, probability=$\[\frac{Favourable}{Possible}=\frac{{}^{7}{{C}_{4}}\times {}^{6}{{C}_{2}}+{}^{7}{{C}_{5}}\times {}^{6}{{C}_{1}}+{}^{7}{{C}_{6}}}{{}^{13}{{C}_{6}}}=0.383\]$

Learn more about probability:

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