You roll two fair dice. Find the probability that the first die is a 6 given that the minimum of the two numbers is a 2.

1/9 = 0.1111 = 11.11% probability that the first die is a 6 given that the minimum of the two numbers is a 2.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

In which

P(B|A) is the probability of event B happening, given that A happened.

is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Minimum of the two numbers is 2.

Event B: First die in a 6.

Fair dice:

Each throw has 6 equally likely outcomes. Thus, in total, there are possible outcomes.

Minimum of the two numbers is a 2.

(2,2), (2,3), (3,2), (2,4), (4,2), (2,5), (5,2), (2,6), (6,2).

9 total outcomes in which the minumum of the two numbers is a two, which means that:

Minimum of the two numbers is a 2, and the first die is a 6.

Only one possible outcome, (6,2). So

Probability that the first die is a 6 given that the minimum of the two numbers is a 2.

1/9 = 0.1111 = 11.11% probability that the first die is a 6 given that the minimum of the two numbers is a 2.

answer is 144

step-by-step explanation:

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation: