Qand r are independent events. if p(q) = 1/4 and p(r)=1/5, find p(q and r)

(b)

Step-by-step explanation:

When two p and q events are independent then, by definition:

P (p and q) = P (p) * P (q)

Then, if q and r are independent events then:

P(q and r) = P(q)*P(r) = 1/4*1/5

P(q and r) = 1/20

P(q and r) = 0.05

In the question that is shown in the attached image, we have two separate urns. The amount of white balls that we take in the first urn does not affect the amount of white balls we could get in the second urn. This means that both events are independent.

In the first ballot box there are 9 balls, 3 white and 6 yellow.

Then the probability of obtaining a white ball from the first ballot box is:

In the second ballot box there are 10 balls, 7 white and 3 yellow.

Then the probability of obtaining a white ball from the second ballot box is:

We want to know the probability of obtaining a white ball in both urns. This is: P( and )  

As the events are independent:

P( and )  = P () * P ()

P( and )  =

P( and )  =

Finally the correct option is (b)

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet