Probability for Math

Introduction to Probability for math:

Probability is a study of math. Probability is number of outcomes divided into total number of events. The probability is also the expected value of the math. These are the two kinds of distribution are used to discrete and continuous distribution.  The general format of the formula for probability math is as follows,

The probability of Event P (A) = `("Number of outcomes n(a)")/("Total Number of events n(s)")`

Probability for Math – Examples:

Probability for math Example 1:

Roll a single dice; find the probability of get number 1.

Solution:

Total Number of possible = n (a) = {1, 2, 3, 4, 5, 6}

n (s) = 6

The number of outcomes n (a) = {6}

n (a) = 1

The probability of getting value = `1/6.`

Probability for math Example 2:

Toss four coins and find the probability of all tails. The possible outcomes are:

Solution:

Step 1:

n (s) = {TTTT, TTTH, TTHT, TTHH, HTTT, HTTH,THHT, HTHH, THTT, TTHH, THHT, HTHH, HTHT, HTHH,HHHT, HHHH }=16

Step 2:

There are 4 tosses with only two tails:

n (a) = { TTTT}=1

Step 3:

Formula:

P (A) = n(a)/n(s)

Answer:

P (A) = `1/16` .

Convert into a decimal 0.0625

The probability of two tails is 0.0625 or Rounded 6%.

Probability for math – Example 3:

The odds in possible of outcomes of an event 9:12.  Find the probability of the outcomes of this event

Solution:

Number of possible outcomes = 9.

Number of non-possible outcomes = 12.

Total number of outcomes = (9+12) = 21.

The probability of Event P (E) = `("Number of outcomes n (a)")/ ("Total Number of events n(s)")`

= `9 / 21.`

Probability for math – Example 4:

A coin is tossed. If the coin ground on top of a container is filled with one black globe and three white spheres. If the coin landed on tails the container is filled with one black sphere and nine white spheres. A sphere is then selected from the container. What is the probability that the sphere selected is black?

Solution:

Let H = Heads, T = Tails and B = Black sphere selected. Then by the law of total probability

P(B)   = P(B|H)P(H) + P(B|T)P(T)

= (0.25)(0.5) + (0.1)(0.5)

P (B)  = 0.175

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Probability for Math - Practice Problems:

Probability for math - Practice Problem 1::

If word chosen at random from a writer X has a character missing with probability 0.1, has a character inserted with probability 0.2, and contains both kinds of error with probability 0.05. What are the probabilities that a letters chosen at random.

Answer:

P (missing or inserted, but not both) = 0.25 - 0.05 = 0.2