Data Science Math Skills, week 4 Quiz Answers.

Probability (basic and Intermediate) Graded Quiz

1. What additional statement, added to the three below, forms a probability                   distribution?

I did not miss my first or second class today.

2. My friend takes 10 cards at random from a 52-card deck, and places them in a box.             Then he      puts  the other 42 cards in a second, identical box. He hands me one of       the       two boxes and       asks me to draw out the top card. What is the probability that the first card     I draw will be the Ace       of   Spades?

1/52

3. I will go sailing today if it does not rain. Are the following two statements Independent or                        dependent?

Dependent

4. The probability that I will go sailing today AND the fair six-sided die will come up even on       the             next  roll is 3

     If these events are independent, what is the probability that I will go sailing today?

$.3$.3.\\\\ If these events are independent, what is the probability that I will go sailing today?

.6

$\text{5. }$$\text{I have two coins. One is fair, and has a probability of coming up heads of}.5$. 

$\text {The second is bent, and has a probability of coming up heads of} .75$. If I toss each coin once, what is the probability that at least one of the coins will come up tails

0.625

6. What is the probability, when drawing 5 cards from a fair 52-card deck, of drawing a "full      house'' (three of a kind and a pair) in the form AAABB?

0.001440576

7. If it rains, I do not go sailing. It rains $10\%$ of days; I go sailing $3\%$ of days.

     If it does not rain, what is the (conditional) probability that I go sailing?

     Written "p(I go sailing | it does not rain)''?

3.333%

8. I am at my office AND not working $2\%$ of the time. I am at my office $10\%$ of the time.             What   is the conditional probability that I am not working, if I am at my office?

20%

9. The factory quality control department discovers that the conditional probability of                 making    a  manufacturing mistake in its precision ball bearing production is $4\%$ on               Tuesday, $4\%$ on Wednesday, $4\%$ on Thursday, $8\%$ on Monday, and $12\%$ on Friday.

    The Company manufactures an equal amount of ball bearings ($20\%$) on each weekday.        What is the       probability that a defective ball bearing was manufactured on a Friday?

37.5

10. An Urn contains two white marbles and one black marble. A marble is drawn from the          Urn without replacement and put aside without my seeing it. Then a second marble is          drawn, and it is white.

      What is the probability that the unknown removed marble is white, and what is the                probability that it  is black?

p(the first marble is white/ the second marble is white) =0.3333

p(the first marble is black/ the second marble is black) =0.667

11.What is the probability, if I flip a fair coin with heads and tails ten times in a row, that I            get       at least 8         heads

$8$