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+y = 29, 5x + 2y = 100

step-by-step explanation:

i'm guessing it was a multiple first option was the correct answer

the answer is; biodiversity resulting from few ancestors

adaptive radiation occurs when a population is subjected to a large natural environment with spatial ecological variations. the parts of the population in the different ecologies begin to adapt to their local environments. due to non-random mating across the large populations, this causes the different populations from the large population to speciate within their local environments. they, therefore, diverge to different species sharing a common ancestor.