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Statistical Probabilities and Distributions
Homework for Prob./Dist. Lesson 3
- Calculate by hand, showing your work, the following combinations:
- 5C3.
- 6C4.
- 9C3.
- 10C4.
- 9C9.
- Calculate by hand, showing your work, the following arrangements:
- 5P3.
- 6P4.
- 9P3.
- 10P4.
- 9P9.
- Calculate the number of different 5-card poker hands that can be
formed from a 52 card deck.
- Calculate the number of different 13-card bridge hands that can be
formed from a 52 card deck.
- A set contains six elements.
How many subsets are there with 0 elements? 1 element? 2 elements? ...
6 elements? Total subsets?
- In a class of 24 students, 7 are left-handed, and the rest right-handed.
If 8 people are selected at random from this group, what is the probability that
- 3 are left-handed and 5 are right-handed?
- all are right handed?
- all are left-handed?
- Etan & Mij, two of the left-handers, are selected?
- A three year old tears the labels off 12 soup cans on her mother's shelf.
Her mother knows there were 3 cans of tomato and 9 cans of vegetable.
The mother selects 4 cans at random.
- What is the probability that exactly 1 of the 4 cans is tomato?
- What is the probability that none of the 4 cans are tomato?
- What is the probability that at least 1 of the 4 cans is tomato?
- The
diagonals
of a convex polygon are made by combining vertices two at time.
However, some of the combinations are sides not diagonals.
How many diagonals are there in a convex
- pentagon?
- heptagon?
- heptadecagon?
- n-gon? Simplify/generalize your answer.
- Dee Monic is a regular customer at the Red Hot Pepper.
The manager figures Dee's probability of ordering
hash browns is 0.7; and eggs 0.55.
What is the probability that (assume independent):
- She does not order hash browns?
- She does not order eggs?
- She orders neither hash browns nor eggs?
- She orders hash browns and eggs?
- She orders either hash browns, or eggs, or both?
- Lois Pass has the following probability of passing various courses:
Chemistry, 80%; Algebra II, 75%; Computer Programming, 90%.
What is the probability of (assume independent)
- passing all 3?
- failing all 3?
- passing at least 1?
- passing exactly 1?
- Untied Harried Lines flies twin-engine airplanes on its routes.
Lab tests show that any one engine has a 0.01 probability (1%)
of failure during any particular flight.
- If the engines operate independently, what is the probability
that both fail?
- Records show both engines fail with probability of 0.001.
What is the probability that the second engine will fail after
the first has already failed?
- Based on part (b) above, do the engines operate independently?
- Three programmers are given a program
which they work on independently
(while occasionally playing interactive games).
The probability of each programmer completing a working program
by the end of the day are 1/4, 2/5, and 1/5, respectively.
Find the probability that at least one working program will be available
by the end of the day.
(Bonus: Find the probability that only one working program will be
available by the end of the day.)