Probabilities Math

Probabilities math

The Probabilities math is the mathematics. This is used to get the expected value of the combination possibles. The Probabilities math is the number of possible outcomes is divided into the total number of outcomes.

Probability =` ("Number of possible outcomes n(a)")/ ("Total number of possibles n(s)")`

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Probabilities math Examples:


Probabilities math – Example 1:

Roll two dice; find the probabilities of Dice are 6 and 1

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

{2,1}{2,2}{2,3}{2,4}{2,5}{2,6}

{3,1}{3,2}{3,3}{3,4}{3,5}{3,6}

{4,1}{4,2}{4,3}{4,4}{4,5}{4,6}

{5,1}{5,2}{5,3}{5,4}{5,5}{5,6}

{6,1}{6,2}{6,3}{6,4}{6,5}{6,6}

n (s) = 36

The number of outcomes n (a) = {6, 1} {1, 6}

n (a) = 2

The probability of getting value = 2/36= 1/18.

Dice Problems:

Probabilities math Example 2:

Roll a single dice; find the probability of get number 4.

Solution:

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

n (s) = 6

The number of outcomes n (a) = {4}

n (a) = 1

The probability of getting value = 1/6.

Coins Problems:

Probabilities math Example 3:

To toss a coin finds to get one tail of the possible outcomes

Solution:

Step 1:

n (s) = {T, H}=2

Step 2:

Tossing a coin with only one head:

n (a) = {T}=1

Step 3:

Formula:

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

Answer:

P (A) = 1/2.

Convert into a decimal 0.5

The probability of one head is 0.5 or Rounded 50%.

Probabilities math – Example 4:

Throw four coins and find the probability of two tails and two heads.

Solution:

Step 1:

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

n (s) = 16

Step 2:

There are 4 tosses with only two tails:

n (a) = { HHTT, TTHH, HTTH, HTTH, }=4

Step 3:

Formula:

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

Answer:

P (A) = 4/16 = 1/4.

Convert into a decimal 0.25

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Practice problems for probabilities math:


Roll two dice; find the probabilities of Dice are not 6 and not 1

Answer:

16/36 (or) 0.4444

2. Roll two dice; find the probabilities of At least one dice isn't 6

Answer:

35/36 (or) 0.9722