Probability

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Ramzi Zeidan
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Hello,
6. One of the objectives of a computer game is to collect keys. There are three stages to the game. The probability
of collecting a key at the first stage is 2/3 , at the second stage is 1/2 , and at the third stage is 1/4 .
(a) Draw a tree diagram to represent the 3 stages of the game.
(b) Find the probability of collecting all 3 keys.
(c) Find the probability of collecting exactly one key in a game.
(d) Calculate the probability that keys are not collected on at least 2 successive stages in a game.
In the latter question, in part (b) in order to find the probability of collecting the 3 keys the simply multiplied the 2/3 1/4 1/2, intuitively, they assumed the events to be independent, why did they do so? And when can I , in general, asssume that two events are independent.
Need a prompt response pleaseeee
Thanks
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Kevin De Bruyne
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(Original post by Ramzi Zeidan)
Hello,
6. One of the objectives of a computer game is to collect keys. There are three stages to the game. The probability
of collecting a key at the first stage is 2/3 , at the second stage is 1/2 , and at the third stage is 1/4 .
(a) Draw a tree diagram to represent the 3 stages of the game.
(b) Find the probability of collecting all 3 keys.
(c) Find the probability of collecting exactly one key in a game.
(d) Calculate the probability that keys are not collected on at least 2 successive stages in a game.
In the latter question, in part (b) in order to find the probability of collecting the 3 keys the simply multiplied the 2/3 1/4 1/2, intuitively, they assumed the events to be independent, why did they do so? And when can I , in general, asssume that two events are independent.
Need a prompt response pleaseeee
Thanks
I understand your question.

The question does not suggest any kind of relationship or dependence between the stages - that's how you would know they are independent:
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