Explanation:

Each of the two coin flips to represent one event. The probability of obtaining exactly one heads and also exactly one tails have the right to be modeled as follows:

Event 1 * event 2

The an essential to knowledge this trouble is to recognize that one of two people heads adhered to by tails, or tails adhered to by heads, would meet the details overall outcome asked for in the problem. Due to the fact that Event 1 will develop either a heads or a tails, we have a 100% possibility of obtaining an end result from occasion 1 that will satisfy one of the two requirements of the certain overall outcome (one heads and also one tails). Occasion 2 will then have actually a 50% chance of producing result that is the opposite, rather than the same, as the outcome of occasion 1. Us can as such calculate the probability of our details overall outcome together follows:

100% * 50%

1 * 0.5

0.5 = 50%

Therefore, the probability the obtaining one heads and also one tails from two coin tosses is 50%.

You are watching: On a multiple choice test with four possible answers for each question what is the probability

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### Example concern #61 : Probability

Assume the you guess: v on each concern of a multiple an option test. There room 12 questions and each question has actually 4 possible answers. What is the probability of getting exactly 8 answer correct?

0.32

0.000004

0.002

0.0002

0.002

Explanation:

This difficulty can be solved using the binomial probability equation:

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### Example concern #1 : Binomial theorem

What is the coefficient of

if the expression
is expanded?

Explanation:

By the Binomial Theorem, if the expression

is expanded, the result deserve to be defined as

If us set

, then the above expression, through slight rearranging, becomes

The coefficient of the

term is

To find the the coefficient of

, us set
and evaluate:

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### Example question #61 : Probability

What is the coefficient of

in the polynomial

Explanation:

The binomial theorem says that we deserve to represent the polynomial

as a sum

Thus, if we want to discover the coefficient that

,

since
,

and
.

Therefore the coefficient of

is

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### Example concern #1 : Binomial theorem

You"re taking a multiple selection quiz that has actually

questions. If each question has actually
choices and also you guess on every one of them, what is the probability of getting precisely
questions correct?

See more: Which Is True About Supporting Details? ? Which Is True About Supporting Details

Explanation:

This inquiry requires the applications of the binomial theorem because that probability. In bespeak to recognize the probability the getting exactly 6 inquiries right, we should remember the formula because that this theorem:

Where

is the variety of trials (total questions),
is the variety of successes (correct answers),
is the probability that success in one attempt (chance of comment a inquiry correctly),
is the probability of fail in one psychological (chance of answering a inquiry incorrectly), and also
is the probability of getting
questions correct out of
total questions. Because there space 5 selections for every question, the opportunities of comment a question appropriately are 1/5, or 0.2, and also therefore the opportunities of comment a question erroneously are 4/5, or 0.8. Currently we have all of our values and also can plug them into the formula:

The first part that the formula in which we have actually a 10 end a 6 in parentheses method we execute the following calculation: