Were is 4,2 and 4,3 4,4 4,5

Mathematics

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2 parts
4.2

120\frac{1}{20}

4.3

7.5%7.5\%

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8 steps

I can help you with 4.2, 4.3, and 4.4. I don't have question 4.5 in the images you sent, so please send it if you'd like me to solve it!

Here are the solutions for the questions you asked about:

Part 4.2· 2 steps

The probability that a randomly selected community hub has cameras and reported vandalism is calculated as follows

  1. Identify the relevant probabilities from the data or the tree diagram.

    P(Cameras Installed)=P(C)=100200=12P(\text{Cameras Installed}) = P(C) = \frac{100}{200} = \frac{1}{2}
    P(Vandalism | Cameras Installed)=P(V∣C)=10100=110P(\text{Vandalism | Cameras Installed}) = P(V|C) = \frac{10}{100} = \frac{1}{10}

  2. Multiply these probabilities to find the joint probability.

    P(C∩V)=P(C)×P(V∣C)=12×110=120P(C \cap V) = P(C) \times P(V|C) = \frac{1}{2} \times \frac{1}{10} = \frac{1}{20}

    The probability is 120\boxed{\frac{1}{20}}.

Part 4.3

7.5%7.5\%

The probability that a community hub did not have cameras and experienced vandalism, as a percentage, is calculated as follows

  1. Identify the relevant probabilities from the data or the tree diagram.

    P(No Cameras Installed)=P(NC)=100200=12P(\text{No Cameras Installed}) = P(NC) = \frac{100}{200} = \frac{1}{2}
    P(Vandalism | No Cameras Installed)=P(V∣NC)=15100=320P(\text{Vandalism | No Cameras Installed}) = P(V|NC) = \frac{15}{100} = \frac{3}{20}

  2. Multiply these probabilities to find the joint probability.

    P(NC∩V)=P(NC)×P(V∣NC)=12×320=340P(NC \cap V) = P(NC) \times P(V|NC) = \frac{1}{2} \times \frac{3}{20} = \frac{3}{40}
  3. Convert the probability to a percentage.

    340×100%=0.075×100%=7.5%\frac{3}{40} \times 100\% = 0.075 \times 100\% = 7.5\%

    The probability is 7.5%\boxed{7.5\%}.

Part 4.4· 3 steps

To determine which group of community hubs has a higher risk of vandalism, we compare the conditional probabilities of vandalism for each group

  1. State the conditional probability of vandalism given cameras installed.

    P(V∣C)=10100=110P(V|C) = \frac{10}{100} = \frac{1}{10}
  2. State the conditional probability of vandalism given no cameras installed.

    P(V∣NC)=15100=320P(V|NC) = \frac{15}{100} = \frac{3}{20}
  3. Compare the two probabilities.

    To compare 110\frac{1}{10} and 320\frac{3}{20}, we can express 110\frac{1}{10} as 220\frac{2}{20}.
    Since 320>220\frac{3}{20} > \frac{2}{20}, the probability of vandalism is higher when no cameras are installed.
    The group of community hubs with a higher risk of vandalism is hubs with no cameras installed. This is because the probability of vandalism given no cameras (P(V∣NC)=320P(V|NC) = \frac{3}{20}) is greater than the probability of vandalism given cameras (P(V∣C)=110=220P(V|C) = \frac{1}{10} = \frac{2}{20}).

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