What is 5/6 and 3/8 as an equivalent fraction
2 answers:
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Answer:
Probability that the wait time is greater than 37 minutes is 0.3474.
Step-by-step explanation:
We are given that the random variable X is known to be exponentially distributed and X be the waiting time for a car to pass by on a country road, where X has an average value of 35 minutes.
<u><em>Let X = waiting time for a car to pass by on a country road</em></u>
The probability distribution function of exponential distribution is given by;
where,
= parameter of distribution.
Now, the mean of exponential distribution is = which is given to us as 35 minutes that means
.
So, X ~ Exp( )
Also, we know that Cumulative distribution function (CDF) of Exponential distribution is given as;
, x > 0
Now, Probability that the wait time is greater than 37 minutes is given by = P(X > 37 min) = 1 - P(X 37 min)
P(X 37 min) =
{Using CDF}
= 1 - 0.3474 = 0.6525
So, P(X > 37 min) = 1 - 0.6525 = 0.3474
Therefore, probability that the wait time is greater than 37 minutes is 0.3474.
Answer: The required probability is 9.09%.
Step-by-step explanation: Given that a jar contains 6 blue, 4 red, and 2 green marbles.
We are to find the probability that three blue marbles are drawn with out replacement.
Total number of marbles = 6 + 4 + 2 = 12.
After drawing one blue marble, we are left with total 11 marbles. And after drawing the second blue marble, we are left with total 10 marbles.
Therefore, the probability of drawing three blue marbles without replacement is given by
Thus, the required probability is 9.09%.