PRACTICE PROBLEMS ON PROBABILITY FOR GRADE 9

Problem 1 :

You are walking along a street. If you just choose a stranger crossing you, what is the probability that his next birthday will fall on a Sunday?

Solution :

Number of days S =  {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}

n(S)  =  7

Let "A" be the event of being birthday on Sunday.

n(A)  =  1

P(A)  =  n(A)/n(S)

P(A)  =  1/7

Problem 2 :

What is the probability of drawing a King or a Queen or a Jack from a deck of cards?

Solution :

Total number of cards n(S)  =  52

Let "A" be the event of getting king or queen or jack card.

n(A)  =  4 + 4 + 4  =  12

P(A)  =  n(A)/n(S)

P(A)  =  12/52

p(A)  =  3/13

Problem 3 :

What is the probability of throwing an even number with a single standard dice of six faces?

Solution :

Sample space  =  {1, 2, 3, 4, 5, 6}

n(S)  =  6

Let "A" be the event of getting even number.

A =  {2, 4, 6}

n(A)  =  3

P(A)  =  n(A)/n(S) 

=  3/6  =  1/2

Problem 4 :

There are 24 balls in a pot. If 3 of them are Red, 5 of them are Blue and the remaining are Green then, what is the probability of picking out (i) a Blue ball, (ii) a Red ball and (iii) a Green ball?

Solution :

Number of balls n(S)  = 24

Let "A", "B" and "C" be the events of getting red, blue and green balls respectively.

n(A)  =  3, n(B)  =  5, n(C)  =  24 - (5 + 3)  =  16

(i)  p(A)  =  n(A)/n(S)

P(A)  =  3/24

P(A)  =  1/8

(ii)  p(B)  =  n(B)/n(S)

P(B)  =  5/24

(iii)  p(C)  =  n(C)/n(S)

P(C)  =  16/24

P(C)  =  2/3

Problem 5 :

When two coins are tossed, what is the probability that two heads are obtained?

Solution :

Outcomes of tossing two coins

S  =  { HH, TT, HT, TH}

n(S)  =  4

Let "A" be the event of getting 2 heads.

A = {HH}

n(A)  =  1

P(A)  =  n(A)/n(S)  

P(A)  =  1/4

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