## 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?

### $.3$

**.6**

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

$\text {The second is bent, and has a probability of coming up heads of} .75$. **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

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