Respuesta :
The required probability for the given event is given as 0.5.
What is probability?
Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lie in the close interval of 0 and 1 [0,1].
Given that,
The probability of a door being locked is 70% = 0.7
Total number of keys is 10.
The number of keys being carried is 2.
Thus, there can be two cases for getting through the door.
Case 1: The door is locked.
The probability to open the door by 1 key is 1/10.
Then, the probability to open the door by 2 keys is 2/10 = 1/5.
Case 2: The door is open.
In this case no keys are needed which means the chance of getting through is the probability of door not being locked which is given as,
1 - 0.7 = 0.3.
Now, the overall probability should consider both the cases as,
P(getting through the door) = P(Door is closed and keys open it)
+ P(The door is open)
= 0.3 + 1/5
= 0.3 + 0.2
= 0.5.
Hence, the probability to get through the door without returning for more keys is 0.5.
To know more about probability click on,
https://brainly.com/question/11234923
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