Roll a die and consider the following two events={2, 3, 6}, event ={1, 5, 6}. are the events e and f independent?
choose the correct answer below.
- no, because the probability of f occurring is higher if it is known that e has occurred.
- no, because there is at least one roll which leads to both e and f occurring.
- yes, because the probability of f occurring is higher if it is known that e has occurred.
- yes, because each roll of the die is an independent event.

Option 1 - No, the probability of F occurring is higher if it is known that E has occurred.

Step-by-step explanation:

Given : Roll a die and consider the following two events={2, 3, 6}, event ={1, 5, 6}.

To find : Are the events E and F independent?

Solution :

E={2, 3, 6}, F={1, 5, 6}

They are not independent event as 6 is common in both the events.

Now, verifying by applying independent property,

Probability of event E is

Probability of event F is

Probability of E and F is

Probability of F occuring when it is known that e has occured.

i.e.

i.e. The probability of F occurring is higher if it is known that E has occurred.

Therefore, The correct option is 1.

Events E and F are not independent, because  the probability of F occurring is higher if it is known that E has occurred.

 The correct option is

(B) No, because there is at least one roll which leads to both E and F occurring.

Step-by-step explanation:  We are given to roll a die and consider the following two events :

A = {2, 3, 6}  and  B = {1, 5, 6}.

We are to check whether the events A and B are independent.

We have

A ∩ B = {2, 3, 6} ∩ {1, 5, 6} = {6}.

So, n(A) = 3,  n(B) = 3  and  n(A ∩ B) = 1.

Since there are 6 elements in the sample space, we get

S = {1, 2, 3, 4, 5, 6}   ⇒   n(S) = 6.

So, the probabilities of the events A, B and A ∩ B are calculated as follows :

Therefore,

Thus, the events A and B are NOT independent because at least one roll which leads to both E and F occurring  and that is 6, common to both A and B.

Option (B) is CORRECT.

x=17

step-by-step explanation:

solve 3x-24=x+10

then that makes it 2x=34 because you subtract an x from both sides to get rid of the one on the right, and then you add 24 to both sides to get rid of the 24 on the left

divide by both sides by 2 to get your answer so that you can get your answer