Answer :
At least one patient will arrive in the following 15 minutes if the next patient arrives before 11:45 a.m.= ∗e −1.5 ≈0.777.
What is Probability?
The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.
The probability of an event can be calculated using the following formula.
Probability(Event) = Positive Results/Total Results = x/n
In order to better grasp probability, let's look at a straightforward application.
Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.
There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.
According to our question-
I If X indicates the number of patients who arrived in 1.5 hours at random, then X = Pois(6*1.5) = Pois (9)
P(X=7)=frac 9/7/7!e-9/approximately 0.17P(X=7)= 7! 9/7
\s ∗e \s−9 \s ≈0.117
(ii) If X indicates the number of patients who arrived in 15 minutes or less, then X = Pois(6*0.25) = Pois (1.5)
At least one patient will arrive in the following 15 minutes if the next patient arrives before 11:45 a.m.
P(X≥1)=1-P(X<1)
=1-P(X=0)
=1-frac 1.5 0 0!*e 1.5 Approximately 0.777P(X1)
=1−P(X<1)
=1−P(X=0)=1− \s0! \s1.5 \s0
\s ∗e \s−1.5 \s ≈0.777
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