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What must the probability of a red light be on this road so that neither road would be preferred over the other on the basis of expected number of red lights?

Sagot :

The probability of a red light be on this road so that neither road would be preferred over the other on the basis of expected number of red lights is 0.3375.

What is Probability:

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Math's to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment. To find the probability of a single event to occur, first, we should know the total number of possible outcomes.

Now,

PDF of a Binomial (n, x) distribution is

given as

p(X=x).[tex]C^n_x P^x (1-p)^(n-x)[/tex]    x =  0,1,2,

Here n = 9, 2:4, p = 0.3

P(x-4)= 9^c_4(0.3)^4 (0.75)^5 = 0·1715 Ans

R Code

We will use the function pGnom() which gives the Cumulative probability of an

Probability  of getting exactly 4 heads is

x <- pGnom (4,9, 0.3) - pGnom (3,9, 0.3)

(We substract 3 to get P(X = 4) since above we have P(X<4) - P(X ≤3)

b)

Expected number in a binomial distribution = np

We  have to equate the Expected values

So

9x0.3 = 8xp

os, p = 0.3375.

To know more about "Probability"

Refer this link:

https://brainly.com/question/13604758

#SPJ4

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