Statistics Binomial Probability. Suppose that in a group of 10 people, each person has a 0.1 probability of having a certain disease, independently from person to person. Now consider a testing plan where the group is split into two groups of 5 people where in each group blood samples are taken from each person, then their blood samples are combined and tested together (so there is one test per group of 5). If a group tests positive for the disease then each person in that group is tested individually for the disease, if a group does not test positive, then the testing is concluded for that group. Let the random variable X represent the total number of tests required with this plan.

Assume that when adults with smartphones are randomly selected, 54% use them in meetings or classes (based on data from an LG Smartphone survey). If 8 adult smartphone users are randomly selected, find the probability that exactly 6 of them use their smartphones in meetings or classes?

Write formula for the sequence of -4, 0, 8, 20, 36, 56, 80, where the order of f(x) is 0, 1, 2, 3, 4, 5, 6 respectively

A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.n=20​,
p=0.7​,
x=19
P(19)=

In binomial probability distribution, the dependents of standard deviations must includes.
a) all of above.
b) probability of q.
c) probability of p.
d) trials.

The probability that a man will be alive in 25 years is 3/5, and the probability that his wifewill be alive in 25 years is 2/3
Determine the probability that both will be alive

How many different ways can you make change for a quarter??
(Different arrangements of the same coins are not counted separately.)

One hundred people line up to board an airplane that can accommodate 100 passengers. Each has a boarding pass with assigned seat. However, the first passenger to board has misplaced his boarding pass and is assigned a seat at random. After that, each person takes the assigned seat. What is the probability that the last person to board gets his assigned seat unoccupied?
A) 1
B) 0.33
C) 0.6
D) 0.5

The value of $(243{)}^{-<!--\; -\; -->\frac{2}{5}}$ is _______.
A)9
B)$\frac{1}{9}$
C)$\frac{1}{3}$
D)0

1 octopus has 8 legs. How many legs does 3 octopuses have?
A) 16
B 24
C) 32
D) 14

From a pack of 52 cards, two cards are drawn in succession one by one without replacement. The probability that both are aces is...

A pack of cards contains $4$ aces, $4$ kings, $4$ queens and $4$ jacks. Two cards are drawn at random. The probability that at least one of these is an ace is A$\frac{9}{20}$ B$\frac{3}{16}$ C$\frac{1}{6}$ D$\frac{1}{9}$

You spin a spinner that has 8 equal-sized sections numbered 1 to 8. Find the theoretical probability of landing on the given section(s) of the spinner. (i) section 1 (ii) odd-numbered section (iii) a section whose number is a power of 2. [4 MARKS]

If A and B are two independent events such that $P(A)>0.5,P(B)>0.5,P(A\cap <!--\; \cap \; -->\stackrel{¯<!--\; ¯\; -->}{B})=\frac{3}{25}P(\stackrel{¯<!--\; ¯\; -->}{A}\cap <!--\; \cap \; -->B)=\frac{8}{25}$, then the value of $P(A\cap <!--\; \cap \; -->B)$ is
A) $\frac{12}{25}$
B) $\frac{14}{25}$
C) $\frac{18}{25}$
D) $\frac{24}{25}$

The unit of plane angle is radian, hence its dimensions are
A) $[M^0{L}^0{T}^0]$
B) $[M^1{L}^{-<!--\; -\; -->1}{T}^0]$
C) $[M^0{L}^1{T}^{-<!--\; -\; -->1}]$
D) $[M^1{L}^0{T}^{-<!--\; -\; -->1}]$

Clinical trial tests a method designed to increase the probability of conceiving a girl. In the study, 340 babies were born, and 289 of them were girls. Use the sample data to construct a 99​% confidence interval estimate of the percentage of girls born?