WRITING SAMPLE SPACE USING TREE DIAGRAMS EXAMPLES

Tree diagram allow us to see visually all possible outcomes of an random experiment. Each branch in a tree diagram represent a possible outcome.

(i) When we throw a die, then from the tree diagram the sample space can be written as

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

When we toss two coins, then fr  om the tree diagram the sample space can be written as

 S = {HH, HT, TH, TT}

Example 1 :

Write the sample space for tossing three coins using tree diagram.

Solution :

The required sample space 

=  {HHH. HHT, HTH, HTT, THH, THT, TTH, TTT}

Total number of outcomes  =  8.

Example 2 :

Write the sample space for selecting two balls from a bag containing 6 balls numbered 1 to 6 (using tree diagram).

Solution :

S = {(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)}

Total number of outcomes  =  36

Example 3 :

If A is an event of a random experiment such that P(A) : P (A bar) = 17 : 15 and n(S) = 640 then find (i) P(A bar ) (ii) n(A).

Solution :

P(A) : P (A bar) = 17 : 15

P(A) / P (A bar) = 17 / 15

P(A) / [1 - P (A)] = 17 / 15

15 P(A)  =  17 [1 - P(A)]

15 P(A)  =  17 - 17 P(A)

15 P(A) +  17 P(A)  =  17

32 P(A)  =  17

P(A)  =  17/32

P(A)  =  n(A) / n(S)

In order to make the denominator of p(A), let us multiply by 20 

P(A)  =  (17/32) ⋅ (20/20)

P(A)  =  340/640

P(A bar)  =  1 - P(A)

=  1 - (340/640)

=  300/640

P(A bar)  =  15/32

n(A)  =  340

Example 4 :

A coin is tossed thrice. What is the probability of getting two consecutive tails?

Solution :

The required sample space 

=  {HHH. HHT, HTH, HTT, THH, THT, TTH, TTT}

n(S)  =  8

Let "A" be the event of getting two consecutive tails

A  =  { HTT, TTH, TTT }

n(A)  =  3

P(A)  =  n(A) / n(S)  

P(A)  =  3/8

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.

©All rights reserved. onlinemath4all.com

Recent Articles

  1. How to Solve Age Problems with Ratio

    Mar 28, 24 02:01 AM

    How to Solve Age Problems with Ratio

    Read More

  2. AP Calculus BC Integration of Rational Functions by Partical Fractions

    Mar 26, 24 11:25 PM

    AP Calculus BC Integration of Rational Functions by Partical Fractions (Part - 1)

    Read More

  3. SAT Math Practice

    Mar 26, 24 08:53 PM

    satmathquestions1.png
    SAT Math Practice - Different Topics - Concept - Formulas - Example problems with step by step explanation

    Read More