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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