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Statistical Probabilities and Distributions

Homework for Prob./Dist. Lesson 3

  1. Calculate by hand, showing your work, the following combinations:
    1. 5C3.
    2. 6C4.
    3. 9C3.
    4. 10C4.
    5. 9C9.

     

  2. Calculate by hand, showing your work, the following arrangements:
    1. 5P3.
    2. 6P4.
    3. 9P3.
    4. 10P4.
    5. 9P9.

     

  3. Calculate the number of different 5-card poker hands that can be formed from a 52 card deck.

     

  4. Calculate the number of different 13-card bridge hands that can be formed from a 52 card deck.

     

  5. A set contains six elements. How many subsets are there with 0 elements? 1 element? 2 elements? ... 6 elements? Total subsets?

     

  6. 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
    1. 3 are left-handed and 5 are right-handed?
    2. all are right handed?
    3. all are left-handed?
    4. Etan & Mij, two of the left-handers, are selected?

     

  7. 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.
    1. What is the probability that exactly 1 of the 4 cans is tomato?
    2. What is the probability that none of the 4 cans are tomato?
    3. What is the probability that at least 1 of the 4 cans is tomato?

     

  8. 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
    1. pentagon?
    2. heptagon?
    3. heptadecagon?
    4. n-gon? Simplify/generalize your answer.

     

  9. 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):
    1. She does not order hash browns?
    2. She does not order eggs?
    3. She orders neither hash browns nor eggs?
    4. She orders hash browns and eggs?
    5. She orders either hash browns, or eggs, or both?

     

  10. 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)
    1. passing all 3?
    2. failing all 3?
    3. passing at least 1?
    4. passing exactly 1?

     

  11. 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.
    1. If the engines operate independently, what is the probability that both fail?
    2. 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?
    3. Based on part (b) above, do the engines operate independently?

     

  12. 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.)

     

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