() for a single roll of two dice, are rolling a sum of 6 and rolling doubles independent events? explain. 

The events, rolling a sum of 6 and rolling doubles are not  independent events

We know that two events A and B are independent if:

where P denotes the probability of an event.

Let A denote the event of rolling a sum of 6

and B denote the event of rolling a double.

Then A∩B denote the event of rolling a double whose sum is 6.

Now we know that there are a total of 36 outcomes on rolling two die

Now

( Since there are 5 outcomes such that sum of the roll is: 6

i.e. (1,5), (2,4) , (3,3) , (4,2) and (5,1) )

Also,

(    Since there are a total of 6 events which are double

i.e.  (1,1) (2,2) (3,3) (4,4) (5,5) and (6,6)  )

This means that:

Also, A∩B is the outcome (3,3)

Hence, we have:

Hence, we get:

         Hence, the events are not independent.

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step-by-step explanation:

the ratio of grapes to blueberries she should use is 12: 3

step-by-step explanation:

if mandie is making 15 cups of fruit salad, the ratio of grapes to blueberries she should use is 12: 3.