# Probability and Solving Systems of Equations

1. A coin is tossed and a die is rolled. What is the probability that the coin shows heads and the die shows a 1 OR a 2?

I tried this one and came up with 1/6 but the OR part is kicking my tail. Maybe I am just over thinking this one.

2. A technician is designing a new portable CD player that requires ten batteries for its power. The probability that any one of these batteries will fail is 0.25. If one battery fails, the CD player will not run. The technician wants to be sure that the CD player will receive enough power from the batteries. What is the probability that of ten batteries, seven with not fail?

3. Let P(n) represent the following statement:

6 + 14 + 22 + ... + (8n-2) = 4n^2 + 2n

In the proof that P(n) is true for all integers n, n > or = 1, which in term must be added

to both sides of P(k) to show P(k+1) follows from P(k)?

4. Find the product, if possible. They are in brackets.

AB, if A = ___, ___ B= ___ ___

I 0 9 -6 I I 7 I

I I I 5 I

I__-0 -10 7 __I I__-2 __I

5. What is the matrix equation of the form Ax=b for the given system of equations?

All equations are inside the same { } on below the other. The subs are below the X

on the right of each one.

{ 3x(sub1) +8x(sub2) + 3x(sub3) - 6x(sub4) = 13 }

-2x(sub1) - 7x(sub2) + 6x(sub3) - 3x(sub 4) = -55

2x(sub1) - 5x(sub2) - 3x(sub3) - 2x*sub4) = -24

4x(sub1) + 2x(sub2) - 9x(sub3) - 5x(sub4) = 19

#### Solution Summary

Probability and Solving Systems of Equations are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.