urgent help

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Hi,

1)Suppose a social network contains a number of people, each of whom has one of two “opinions” (e.g. a preference for Mac versus PC). Each person is connected with a set of “friends”, some of the other people in the network. You can choose any person in the network and let them see the opinions of their friends, and if most of the friends have the same opinion, then the chosen person will change their opinion to the one shared by the majority of their friends. If there’s an equal split, you can choose their opinion. Assuming the network is connected, can we always find a sequence of people so as to ensure that they all end up with the same opinion?

2)Two ants walk on a line in a random fashion. They begin 10cm apart. At each time step, each ant has a probability of 1/2 to move 1cm to the left, and probability 1/2 to move 1cm to the right. What is the probability that after 7 time steps, the ants have met one another (i.e., passed through the same point)?

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I have read the above description . I only need help not answers as i wrote in my question . Please read again . I wrote i need help , so i should be helped before directing me to read such instructions again thanks

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You will likely get a better response if you post what you've tried and where you feel you are running into issues.

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2 hours ago, anum said:

1)Suppose a social network contains a number of people, each of whom has one of two “opinions” (e.g. a preference for Mac versus PC). Each person is connected with a set of “friends”, some of the other people in the network. You can choose any person in the network and let them see the opinions of their friends, and if most of the friends have the same opinion, then the chosen person will change their opinion to the one shared by the majority of their friends. If there’s an equal split, you can choose their opinion. Assuming the network is connected, can we always find a sequence of people so as to ensure that they all end up with the same opinion?

Hint

Have you drawn a tree diagram.

Can you find a spanning tree?

2 hours ago, anum said:

2)Two ants walk on a line in a random fashion. They begin 10cm apart. At each time step, each ant has a probability of 1/2 to move 1cm to the left, and probability 1/2 to move 1cm to the right. What is the probability that after 7 time steps, the ants have met one another (i.e., passed through the same point)?

Hint

Change the description of what happens at each step.

They move closer (in how many ways)

They move further apart (in how many ways)

Assign probabilities to each.