Tips on cracking Aptitude Questions on Probability

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3 TIPS on cracking Aptitude Questions on
Probability
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Tip 1 Categorize the events as mutually
dependent, independent or exclusive
Mutually Dependent Events 2 or more events are
that are such that the occurrence of one affects
the occurrence of the other. The words and,
together, all, etc. indicate that the events
are mutually dependent. Example Let a card is
chosen at random from a standard deck of 52
playing cards. Without replacing it, a 2nd card
is chosen. The probability of choosing any card
is 1 out of 52. However, if the 1st card is not
replaced, then the 2nd card is chosen from only
51 cards. Accordingly, the probability of
choosing another card is 1 out of 51. Thus, these
events are mutually dependent. Mutually
Independent Events 2 or more events such that
the occurrence of one does not affect the
occurrence of the other. If the problem is such
that after each event, the sample space is
restored to its original state, then the events
are mutually independent. Example In the above
example, the 1st card that was drawn is replaced
before drawing the 2nd card. The probability of
choosing any card is 1 out of 52. Now, the 1st
card is replaced, then the 2nd card is chosen
from 52 cards again. Accordingly, the probability
of choosing another card is 1 out of 52. Thus,
these events are mutually independent. Mutually
Exclusive Events 2 or more events that cannot
happen simultaneously. The indicative words are
or, at most, at least, etc. Example The
events running forward and running backwards
are mutually exclusive. Similarly, you cant toss
a coin and get both a heads and tails at the same
time, so tossing a heads and tossing a tails
are mutually exclusive.
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Tip 2 Probability of occurrence of mutually
exclusive events is the sum of their individual
probabilities
Question Three unbiased coins are tossed. What
is the probability of getting at most two
heads? Solution Probability of getting at most
2 heads Probability of getting no head
Probability of getting 1 head Probability
of getting 2 heads Probability of getting no
heads Probability of getting all tails ( ½ )(
½ )( ½ ) 1/8 Probability of getting 1 head
C(3,1)( ½ )( ½ )( ½ ) 3/8 Probability of
getting 2 heads C(3,2)( ½ )( ½ )( ½ )
3/8 Thus, required probability 1/8 3/8 3/8
7/8 Question Two dice are thrown
simultaneously. What is the probability of
getting two numbers whose product is
even? Solution There might be 2 cases both
numbers are even or one is even and the other is
odd. Probability that both no.s are even
(3/6)(3/6) ¼ Probability that one is even and
the other is odd (3/6)(3/6) x 2 ½
Probability of getting 2 no.s whose product is
even ¼ ½ ¾
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Tip 3 Probability of occurrence of mutually
dependent or independent events is the product of
their individual probabilities
Question Two cards are drawn together from a
pack of 52 cards. What is the probability that
one is a spade and one is a heart? Solution Prob
ability of getting a Spade 13 / 52 ¼ Now,
probability of getting a Heart 13/51 Since the
order of getting the cards is not mentioned, both
the orders count. Probability of getting a Spade
and a Heart 2 x (¼)(13/51) 13 /
102 Question A bag contains 4 white, 5 red and
6 blue balls. Three balls are drawn at random
from the bag. Find the probability that all of
them are red. Solution Total no. of balls
456 15 Probability of drawing a red ball at
1st draw 5/15 1/3 Probability of drawing a
red ball at 2nd draw 4/14 2/7 Probability of
drawing a red ball at 3rd draw 3/13 Probability
of drawing all 3 red cards 1/3 x 2/7 x 3/13
2/91
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