A study of immunizations among school‑age children in California found that some areas had rates of unvaccinated school‑age children as high as 13.5 % in 2014. Imagine a classroom of 20 children in one such area where 13.5 % of children are unvaccinated. If there are no siblings in the classroom, we are willing to consider the vaccination status of the 20 unrelated children to be independent. A) Obtain the probability that none of the 20 children in such classroom would be unvaccinated

B) Obtain the probability that at least one of the 20 children in such a classroom would be unvaccinated.

a)

b)

And we can use the complement rule and we have this:

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

The probability mass function for the Binomial distribution is given as:  

Where (nCx) means combinatory and it's given by this formula:  

The complement rule is a theorem that provides a connection between the probability of an event and the probability of the complement of the event. Lat A the event of interest and A' the complement. The rule is defined by:

Solution to the problem

For this case we define the random variable X="number of children unvaccinated" and the distribution for X is given by:

Part a

For this case we want this probability:

Using the probability mass function we can replace and we got:

Part b

For this case we want this probability:

And we can use the complement rule and we have this:

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

~

if the probability is 1/12, 75 people will receive a $25 gift card

step-by-step explanation: