Solves Examples on Probability

Example 1:

Three coins are tossed simultaneously Find the probability that

(i) no head                               (ii) one head                                        (iii) two heads

(iv)     atleast two heads.             (v) atmost two heads appear.

Solution:

The sample space for the 3 coins is

S = { HHH, HHT, HTH, HTT, THH, THT, TTH, TTT} ; n(S) = 8

(i)                   No head appear A = {TTT}; n(A) = 1

\P(A) = 1/8

(ii)                 One head appear B = {HTT, THT, TTH}; n (B) = 3

\P(B) = 3/8

(iii)                Two heads appear C = {HHT, HTH, THH}; n(C)=3

\P(C) = 3/8

(iv)                Atleast two heads appear

D = { HHT, HTH, THH, HHH}; n(D) = 4

                P (D)      4/8 =1/2               

(v)                 Atmost two heads appear E = { TTT, HTT, THT, TTH,HHT, HTH,THH} n(E) = 7

\P(E) =  7/8

Example 2:

When two dice are thrown, find the probability of getting doublets (Same number on

both dice)

Solution:

When two dice are thrown, the number of points in the sample space is n(S) = 36 Getting doublets: A = {(1,1) , (2,2) , (3,3) , (4,4) , (5,5) , (6,6)}

\P(A) =   6/36 = 1/6

Example 3:

A card is drawn at random from a well shuffled pack of 52 cards. What is the probability that it is (i) an ace (ii) a diamond card

Solution:

We know that the Pack contains 52 cards \ n(S) = 52

(i)    There are 4 aces in a pack. n(A) = 4

\P(A) =  4/52 =1/13

(ii)     There are 13 diamonds in a pack \ n(B) = 13

\P(B) =  13/52 = 1/4

Example 4:

A ball is drawn at random from a box containing 5 green, 6 red, and 4 yellow balls. Determine the probability that the ball drawn is (i) green (ii) Red (iii) yellow (iv) Green or Red (v) not yellow.

Solution:

Total number of balls in the box = 5 + 6 + 4 = 15 balls

(i)	Probability of drawing a green ball = 5/15 =1/3
(ii)	Probability of drawing a red ball= 6/15 = 2/5
(iii) (iv)	Probability of drawing a yellow ball=4/15 Probability of drawing a Green or a Red ball

               5/15 + 6/15 = 11/15