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Probability of drawing a card, mutually exclusivity and probability distributions

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If one card is drawn from a deck, find the probability of getting these results.
a- An Ace
b- A diamond
c- An ace f diamonds
d- A 4 or a 6
e- 4 or a club
f- A 6 or a spade
g- A heart or a club
h- A red queen
i- A red card or a 7
j- A black card or a 10

If four students are seated on a bench, find the probability that the students are seated in alphabetical order from left to right, according to each student¡¯s last name.
(Assume that all the last names are different)

A couple plans to have 3 children, find each probability
A. Of all boys
B. Of all girls or all boys
C. Of exactly two boys or two girls
D. Of at least one child of each gender

Give an example of two events that are mutually exclusive and two events that are not mutually exclusive.

An automobile sales woman finds that the probability of making a sale is 0.23. If she talks to four customers today, find the probability that she will sell four automobiles.

If two people are selected at random, find the probability that they have the same birthday (both month and day)

If a family has four children, find the probability that there is at least one girl among the children

Determine whether the distribution represents a probability distribution. If it is not state wide.

X 6 12 18
___________________________
P(X) 1/4 1/16 3/16

X 1 3 5 7 9 1 _____________________________________________________________
P(X) 1/6 1/6 1/6 1/6 1/6 1/6

Construct a probability distribution for the data, and draw a graph for the distribution.
The probability that a customer selects 1,2,3,4, or five items at a convenience store are 0.32, 0.12, 0.23, 0.18 and 0.15, respectively

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Solution Summary

The solution includes multiple problems involving statistics, probability, distributions, definitions of concepts, and random variables.

Solution provided by:
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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