STAT 100A Lecture 6: Independent Events Notes

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graygnu278

15 Apr 2016

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Two events, a and b, are said to be independent if. P(a|b) = p(a) if and only if a and b are independent. If a and b are independent, then so are a and b, a and b, a. Let a be the event that the sum of the results of the dice is 6. Let b be the event that the result of the rst die is 4. Let c be the event that the sum of the results of the dice is 7. There are 10 books in a library, 8 of type a and 2 of type b. On a day when one of the books is missing, alice enters the library, randomly takes a book, reads it and returns it. After alice returns the book, bob enters the library and randomly takes a book. Let e be the event that alice took a book of type a.

Related Questions

9. Identify why this assignment of probabilities can not be legitimate.

a. P(A & B) can not be greater than either P(A) or P(B).

b. A and B are not given as mutually exclusive events.

c. P(A|B) is not known.

d. A and B are not given as independent events.

e. none of these.

10. Suppose a box contains 3 detective light bulbs and 12 good bulbs. Two bulbs are chosen from the box without replacement. Find the probability that one of the bulbs drawn is good and one is defective.

A. 12/35

B. 6/35

C. 3/14

D. 3/70

E. None of these

ceruleansea-lion635

Two fair dice are tossed, and the up face on each die is recorded.

a. List the 36 sample points contained in the sample space.

b. Assign probabilities to the sample points.

c. Find the probability of observing each of the following events:

A: {A 3 appears on each of the two dice.}

B: {The sum of the numbers is even.}

C: {The sum of the numbers is equal to 7.}

D: {A 5 appears on at least one of the dice.}

E: {The sum of the numbers is 10 or more.}

burgundyguinea-pig688

Suppose two dice (one red, one green) are rolled.

Consider the following events. A: the red die shows 1; B: the number add to 4; C: at least one of the numbers is 1; and D: the numbers do not add to 11. In express the stated event in symbolic form and say how many elements it contains [Hint: See Example]

The red die shows 1, but numbers do not add to 11.

whitekangaroo912

STAT 100A Lecture 6: Independent Events Notes

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