Using time dependent perturbation theory, estimate the ratio of the probability of a transition to a 3p orbital compared to that to a 2p orbital when a hydrogen atom in its ground electronic state is exposed to 105nm light for 1 femptosecond. What is the ratio for a 2 femptosecond exposure? Explain the difference. (Hint: orbital functions in addition to energy differences need to be considered; an integral table is also helpful)

The probability that a randomly selected box of a certain type of cereal has a particular prize is 0.2. Suppose you purchase box after box until you have obtained four of these prizes.

(a)

What is the probability that you purchase x boxes that do not have the desired prize?

h(x; 4, 0.2)

b(x; 4, 2, 10)

nb(x; 4, 2, 10)

b(x; 4, 0.2)

h(x; 4, 2, 10)

nb(x; 4, 0.2)

(b)

What is the probability that you purchase six boxes? (Round your answer to four decimal places.)

.256

(c)

What is the probability that you purchase at most six boxes? (Round your answer to four decimal places.)

(d)

How many boxes without the desired prize do you expect to purchase?

How many boxes do you expect to purchase?

For a normal distribution where μ = 100 and σ = 10, what is the probability of:
1. P (X> 80) =
2. P (95 <X <105) =
3. P (X <50) =
4. P (X <100) =
5. P (X <90 and X> 110) =
6.P (X> 150) =

1. Ross shuffles a deck of cards. what is the probability that the queen of hearts is the top card or the jack of spades is the bottom card of the deck?

2. Lindsey has ten PAIRS of shoes in her closet, each being a different brand. If she randomly picks 5 SHOES without replacement, what's the probability she will have one or more matching pairs?

3. A bag contains 100 bills 80 of which are authentic bills and 20 of which are fake. Bills are drawn randomly without replacement. What's the probability that exactly two fake bills are drawn before the third authentic bill is drawn?

4. There are n people in a room. Each takes their shoes off and puts them in a urn. if each person then selects two random shoes without replacement from the urn, what's the probability everyone has their own shoes?

The equilibrium electron concentration is given by the product of density of states and probability function, n(E) = g_c(E)F(E)n(E)=gc​(E)F(E) whereg_c(E)gc​(E) and F(E)F(E) are the conduction band density of states and Fermi-Dirac probability function, respectively

Using the full expression of Fermi-Dirac function, calculate the energy relative to the conduction band edge, E-E_cE−Ec​, at which the electron concentration becomes maximum. This semiconductor has a bandgap of 1.124 eV and the temperature is 300 K. Further assume that the Fermi level, E_FEF​ is located precisely at the middle of the bandgap, i.e. E_C - E_F = \frac{E_g}2EC​−EF​=2Eg​

Find the probability for Z<1.14 given that Z is Standard Normal Distribution?

Must be calculated in R

In twenty prey visits on carnivorous plants, if the probability of a capture in one visit is 0.2, what is the probability to have 3 to 6 captures ,
or P(3 less or equal than X less or equal than 6).

Determine whether or not the distribution is a discrete probability distribution and select the reason why or why not.

Answer

First, decide whether the distribution is a discrete probability distribution, then select the reason for making this decision.

Decide Yes No

Reason Since the probabilities lie inclusively between 0 and 1 and the sum of the probabilities is equal to 1. Since at least one of the probability values is greater than 1 or less than 0. Since the sum of the probabilities is not equal to 1. Since the sum of the probabilities is equal to 1. Since the probabilities lie inclusively between 0 and 1.

Of the two officers selected from a group of officers, the probability of the first being male and the second being female is 1/4. Since the ratio of male civil servants to female civil servants is 1/2, how many civil servants are there in the group? b) One bag contains 6 white and 4 black balls. What is the probability that one of the 3 balls drawn randomly from this bag is white and the other two are black?