Guests at the white house have to clear four layers of security by the secret service: two identity checks, a dog sniff check, and a metal detection check with an x-ray machine. historically 16% of the people in line are tourists and the rest are guests. all tourists are filtered out at the identity checkpoints, so they are not going through the dog and x-ray checkpoints. the dog check results in an alarm for 20% of the people in line. guests who trigger a dog alarm also trigger an x-ray alarm with probability 1/10. guests who do not trigger a dog alarm trigger an x-ray alarm with probability 1/16. what is the probability that a guest who triggers an x-ray alarm also triggers a dog alarm?

0.6863

Step-by-step explanation:

Let A and B be the events

A = the dog check alarm is triggered

B= the x-ray alarm is triggered

As guests who trigger a dog alarm also trigger an x-ray alarm with probability 1/10, we have P(A∩B) = 0.1 .

The dog alarm can only be triggered by a guest, so we want to find P(A|B) , the probability that a guest triggers the dog alarm given that she triggered the x-ray alarm.

But

So we only need to find P(B) to find P(A|B) out.

Since 16% of people (tourists) in line are filtered out before reaching the dog alarm, only 84% of people (guests) reach the dog alarm. That is to say, 16% of 84% = 13.44% of people in line reach the dog alarm.

Since the dog check results in an alarm for 20% of the people in line, 20% of 13.44% = 2.688% of people in line (guests) trigger the dog alarm, so

P(A) = 0.02688.

Since guests who do not trigger the dog alarm trigger an X-ray alarm with probability 1/16, we have P(B|) = 0.0625.

We have then the following:

But and are disjoints sets whose union is B, so

and finally

which expression can be used to convert 80 us dollars (usd) to australian dollars (aud)?

1 usd = 1.0343 aud

1 aud = 0.9668 usd

step-by-step explanation:

sorry just need the points

8

step-by-step explanation:

to find the amount of gift bags to use all the supplies, find the gcf or greatest common factor. this is the largest number which multiplies evenly into each term.

48 has factors: 1, 2, 3, 4, 6, 8, 12. 16, 24, 48

80 has factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

64 has factors: 1, 2, 4, 8, 8, 16, 32, 64

the highest number factor they all share in common is 8. this means there will be 8 bags with 6 pencils, 10 markers, and 8 stickers in each bag.