I roll a standard six-sided die 6 times in a row. What is the probability that the numbers alternate between odd and even?
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1 / 64

Step-by-step explanation:

The probability of a multi-stage events that are independent is the product of all of them. Probability is basically the desirable outcomes over the total outcomes. When rolling a die, there are 6 different numbers you can roll, meaning six different outcomes. There are 3 outcomes where you can roll an even number: 2, 4, and 6. And it's the same with odd numbers: 1, 3, and 5. So the probability of rolling an even number is 3 / 6 or 1 / 2 and the probability of an odd number is the same, 1 / 2. Now, since the probabilities are the same at each stage, we can multiply 1 / 2 to itself 6 times or (1/2)^6 which evaluates to 1 / 64.

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.

a

step-by-step explanation: