Suppose that the probability of a company supplying a defective product is a and the probability that the supplied product is not defective is b. Before each product supplied is released for further use, it must be screened through a system which detects the potential defectiveness of the product. The probability that this process successfully detects a defective product is x, and the probability that it does not is y. What is the probability that at least one defective product will pass through the system undetected after 20 products have been screened?

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?