100 students are divided into 2 groups one of 60 and other of 40 .find rhe probability that you and your friend are in the same group.
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You could be in the group of 40 people with a probability of 4010040100. After already being picked to be in this group, the probability of your friend being in this group is 39993999.
The second thing that could happen is that you are picked to be in the group of 60 people. This can happen with a probability of 6010060100. Again, your friend will be in this group with a probability of 59995999.
The final answer is then
(40100⋅3999)+(60100⋅5999)≈51.51%(40100⋅3999)+(60100⋅5999)≈51.51%
You can think about it this way. You are going to be in some group. Now let us find the probability of your friend being in the same group. To solve the problem, you give weights to the different situations, that is, you could be in group one with a probability of .4.4 and then find the combined probability of your friend being in the same group. Similarly, apply the same for the next situation.
Hope that helps you out.
The second thing that could happen is that you are picked to be in the group of 60 people. This can happen with a probability of 6010060100. Again, your friend will be in this group with a probability of 59995999.
The final answer is then
(40100⋅3999)+(60100⋅5999)≈51.51%(40100⋅3999)+(60100⋅5999)≈51.51%
You can think about it this way. You are going to be in some group. Now let us find the probability of your friend being in the same group. To solve the problem, you give weights to the different situations, that is, you could be in group one with a probability of .4.4 and then find the combined probability of your friend being in the same group. Similarly, apply the same for the next situation.
Hope that helps you out.
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