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7 Basic Probability Problems

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See the attached file.
1. A certain coin has the same probability of landing heads as it does landing tails - but this coin is special, because it also has a 30% chance of landing on its side.
a. What is the probability of this coin landing heads?
b. What are the odds against this coin landing on its side?
c. If this coin is tossed twice, what is the probability of it landing on its side both times?
d. If this coin is tossed twice, what is the probability of it not landing on its side either time?

2. Each airport across the country has its own 6 digit code #(Manchester314552/Chicago121055). How many different codes can be made, if zero is not allowed as a first digit?

3. Professor Brown gives her students a maximum of 3 attempts to pass a final exam. She has found that the probability of passing on the first attempt is .60, the probability of passing on the second try is .68, and the probability of passing on the third attempt is .85. What is the probability that a randomly selected student of hers will pass the final exam?

4. A sample space is composed of four possible outcomes, called A, B, C, and D. A and B are equally likely, D is four times as probable as A, and C is five times as probable as A. What is the probability of outcome A?

5. Let P(4) be the probability of getting a four when you choose a card from a deck of cards, let
P(F) be the probability of getting a face card from a deck, and P(H) be the probability of getting a heart from the deck.
a. What is P(4 or H)?
b. What is P(4 or F)?
c. What is P(H or F)?
d. Are events 4 and H mutually exclusive?
e. Are events 4 and F mutually exclusive?
f. Are events 4 and H independent?
g. Are events 4 and F independent?

6. 30% of the trees in a particular forest have a disease, 40% are too small to be used for lumber, and 22% are both small and diseased. What % are too small to be used for lumber or have a disease?

7. The ages of students enrolled in the classes at a local community college are given in the following chart.
18-27 28-37 38-47 47+
Male 425 265 125 54
Female 471 149 98 25

Find: a. P(male or 28-37)
b. P(female or 38+)
c. P(18-27 given the person is female)
d. P(28-47)
e. P(47+ and female).

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This posting provides solution to 7 basic various probability problems.

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1. A certain coin has the same probability of landing heads as it does landing tails - but this coin is special, because it also has a 30% chance of landing on it's side.
a.What is the probability of this coin landing heads?
Solution. Denote by P(H), P(T) and P(S) the probabilities with head, tail and side, respectively. We know that P(H)=P(T) and P(S)=30% but P(H)+P(T)+P(S)=1, so
P(H)=P(T)=[1-30%]/2=35%

b.What are the odds against this coin landing on it's side?
Since P(S)=30%, the odds against this coin landing on it's side is 3 : 7

c.If this coin is tossed twice, what is the probability of it landing on it's side both times?

Assume that the experiments are done independently, we know that the probability of it landing on it's side both times is 30%*30%=9%

d.If this coin is tossed twice, what is the probability of it not landing on it's side either time?

Each time it is NOT landing on it's side with probability 1-30%=70%, so the probability of it not landing on it's side either time is 70%*70%=49%

2. Each airport across the country has its own 6 digit code #(Manchester314552/Chicago121055). How many different codes can be made, if zero is not allowed as a first ...

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  • 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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