Please solve the following probability problem. Show all work and must solve all parts HW 1.z. (Mingle)A number is called and players need to group up and enter rooms. Ifplayers do not manage to make it into the rooms in time, or if a room hasless or more players than it is supposed to have, they will be eliminated.Assume there are 200 people other than you and the number called is 10.Determine the probability that you will form the group of the correct sizein each of the following cases:a) Imagine you had no better strategy than going to each of the 200people and tossing a fair coin to determine if they will join yourgroup or not.b) Imagine everybody else is divided into 25 groups of 4 people and 20groups of 5 people. Among all the possible groups, you are choosingto join two at random.c) Imagine everybody else is divided into 20 groups of 4 people, 10groups of 2 people and 20 groups of 5 people. You are choosing tojoin two groups at random.d) Imagine everybody else is divided into 20 groups of 4 people, 10groups of 2 people and 20 groups of 5 people. You are choosing tojoin three groups at random.e) Imagine everybody else is divided into 20 groups of 4 people, 10groups of 2 people and 20 groups of 5 people. You are choosing tojoin two groups at random but only choose the third group at randomif at the moment you have less than 10 players in your group.
Please solve the following probability problem. Show all work and must solve all parts
HW 1.z. (Mingle)
A number is called and players need to group up and enter rooms. If
players do not manage to make it into the rooms in time, or if a room has
less or more players than it is supposed to have, they will be eliminated.
Assume there are 200 people other than you and the number called is 10.
Determine the probability that you will form the group of the correct size
in each of the following cases:
a) Imagine you had no better strategy than going to each of the 200
people and tossing a fair coin to determine if they will join your
group or not.
b) Imagine everybody else is divided into 25 groups of 4 people and 20
groups of 5 people. Among all the possible groups, you are choosing
to join two at random.
c) Imagine everybody else is divided into 20 groups of 4 people, 10
groups of 2 people and 20 groups of 5 people. You are choosing to
join two groups at random.
d) Imagine everybody else is divided into 20 groups of 4 people, 10
groups of 2 people and 20 groups of 5 people. You are choosing to
join three groups at random.
e) Imagine everybody else is divided into 20 groups of 4 people, 10
groups of 2 people and 20 groups of 5 people. You are choosing to
join two groups at random but only choose the third group at random
if at the moment you have less than 10 players in your group.
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