1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Salsk061 [2.6K]
3 years ago
12

A teacher teaches two classes with 8 students each. Each student has a 95% chance of passing their class independent of the othe

r students. Find the probability that, in exactly one of the two classes, all 8 students pass.
Mathematics
1 answer:
dsp733 years ago
3 0

Answer:

0.4466 = 44.66% probability that, in exactly one of the two classes, all 8 students pass.

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they pass, or they do not. The probability of an student passing is independent of other students, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

Probability that all students pass in a class:

Class of 8 students, which means that n = 8

Each student has a 95% chance of passing their class independent of the other students, which means that p = 0.95

This probability is P(X = 8). So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 8) = C_{8,8}.(0.95)^{8}.(0.05)^{0} = 0.6634

Find the probability that, in exactly one of the two classes, all 8 students pass.

Two classes means that n = 2

0.6634 probability all students pass in a class, which means that p = 0.6634.

This probability is P(X = 1). So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 2) = C_{2,1}.(0.6634)^{1}.(0.3366)^{1} = 0.4466

0.4466 = 44.66% probability that, in exactly one of the two classes, all 8 students pass.

You might be interested in
APT4PTO
inysia [295]

Answer:

  1536 square inches

Step-by-step explanation:

In units of 5 feet, the backdrop is 3 units wide and 2 units high, for a total area of 3×2 = 6 square units.

Those same units on the scale drawing are each 16 inches. One square unit on the scale drawing is (16 in)² = 256 in². So, 6 of them have an area of ...

  6 × 256 in² = 1536 in²

6 0
3 years ago
Simplify the expression:<br><br> 6(1 + 2b) =
timama [110]

Answer:

6+12b

Step-by-step explanation:

i took a test with this question and got it right

5 0
3 years ago
Which value can be added to the set below without changing its mean?
Ipatiy [6.2K]
The answer you are looking for is B. 15
6 0
3 years ago
Read 2 more answers
Y varies directly as x y = 120 when x = 8 find y when x = 14
ANTONII [103]

Answer:

y = 120

Step-by-step explanation:

this is the formula

y = kx

now insert the numbers to find k

120 = k8

120/8

k = 15

now insert 15 into the equation where k was

y = 15 x 14

y = 210

3 0
3 years ago
At a school camp there is enough foot for 150 students for 5 days.
weeeeeb [17]

Answer:

<h3 />

Step-by-step explanation:

you need to find how much food is used for 1 person then times that answer by 100 to find how much food is needed

4 0
3 years ago
Other questions:
  • 1. ) Consider the function f(x)=5−7x2,−5≤x≤1
    7·1 answer
  • Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the corre
    12·2 answers
  • Please help me with this question
    7·2 answers
  • Use the exact values of the ratios and find the value of tan 45° + sin 30°​
    13·2 answers
  • Use the graph that shows the solution to f(x)=g(x)
    9·1 answer
  • Find the coordinates of T' after the given translation.
    15·1 answer
  • The coordinates of L and M are (3, 6) and (9, 8) respectively. X is the mid-point of LM, determine the coordinate of the point X
    12·1 answer
  • Pleaseee help
    6·2 answers
  • A store owner sold 4 paint brushes for $12.00 and 8 pens for $3 20. What is the difference between the unit price of a paint bru
    9·2 answers
  • A sequence is defined recursively using the formula f(n 1) = f(n) – 5 . which sequence could be generated using this formula? 1,
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!