I ONLT NEED NUMBER 4 PLEASE I ONLT NEED NUMBER 4 PLEASE Exercises for Section 2.

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I ONLT NEED NUMBER 4 PLEASE

I ONLT NEED NUMBER 4 PLEASE

Exercises for Section 2.3 I. Let A and B be events with P(A) = 0.8 and P(A n B) = 0.2. For what value of P(B) will A and B be independent? 6. 2. Let A and B be events with P(A)0.5 and P(A n B*) = 0.4. For what value of P(B) will A and B be independent? 3. A box contains 15 resistors. Ten of them are labeled 50 S2 and the other five are labeled 100 S2 a. What is the probability that the first resistor is 100 ? b. What is the probability that the second resistor is 100 S2, given that the first resistor is 50 S2? c. What is the probability that the second resistor is 7. S 100 , given that the first resistor is 100 ? ar ha tu th a. 4. Refer to Exercise 3. Resistors are randomly selected from. the box, one by one, until a 100 resistor is selected. a. What is the probability that the first two resistors are both 50 S2? are selected from the box? tors are selected from the box? b. What is the probability that a total of two resistors b. c. What is the probability that more than three resis- 5. On graduation day at a large university, one graduate is selected at random. Let A represent the event that the student is an engineering major, and let B repre- 8. A tha end pro the sent the event that the student took a calculus course

Explanation / Answer

4:

Thera are total 15 resistors in the box out of which 10 are 50 ohm and five are of 100 ohm.

(a)

Here resistors are selected without replacement so the probabiltuy of selecting first two resistors of 50 ohms and third of 100 ohm is:

P(first two are of 50 ohm) = (10/15) * (9/14) * (5/13) = 0.1648

(b)

The total of two resistors are selected in case if first one is of 50 ohm and second one is of 100 ohm. Here resistors are selected without replacement so the probabiltuy of selecting that two resistors are selected is:

P(two exactly) = (10/15) * (5/14) = 0.2381

(c)

The probability that more than three resistors are selected from the box will be complement of at most three resistors are selected.

P(more than three resistors) =1 - P(at most resistors) = 1- [ (5/15) + (10/15) * (5/14) + (10/15) * (9/14) * (5/13) ] = 0.2637

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