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# Probability Example 3

Shortcut tricks on probability are one of the most important topics in exams. Time takes a huge part in competitive exams. If you know how to manage time then you will surely do great in your exam. Most of us skip that part. We provide examples on Probability shortcut tricks here in this page below. We try to provide all types of shortcut tricks on probability here. Visitors are requested to carefully read all shortcut examples. You can understand shortcut tricks on Probability by these examples.

Before doing anything we recommend you to do a math practice set. Then find out twenty math problems related to this topic and write those on a paper. Do first ten maths using basic formula of this math topic. You also need to keep track of timing. After finish write down total time taken by you to solve those ten maths. Now practice our shortcut tricks on probability and read examples carefully. After this do remaining ten questions and apply shortcut formula on those math problems. Again keep track of Timing. You will surely see the improvement in your timing this time. But this is not all you need. If you need to improve your timing more then you need to practice more.

Math section in a competitive exam is the most important part of the exam. It doesn’t mean that other topics are not so important. But only math portion can leads you to a good score. A good score comes with practice and practice. You should do your math problems within time with correctness, and this can be achieved only by using shortcut tricks. But it doesn’t mean that you can’t do math problems without using any shortcut tricks. You may have that potential that you may do maths within time without using any shortcut tricks. But so many other people may not do the same. Here we prepared probability shortcut tricks for those people. We try our level best to put together all types of shortcut methods here. But it possible we miss any. We appreciate if you share that with us. Your little help will help others.

Example #1
A brother and his sister appear in an interview for two vacancies in the same post. The probability of brother’s selection is 1 / 7 and the probability of sister’s selection is 1 / 5. What is the probability that only one of them is selected?

1. 1 / 7
2. 2 / 7
3. 3 / 7
4. 5 / 7

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Answer: Option (B)
How to Solve
Let, A be the event that the Brother is selected.
And, B be the event that the Sister is selected.

p(A) = 1 / 7.
p(B) = 1 / 5.

Probability of brother is not selected is,
( 1 – 1 / 7 )
= 6 / 7.

Probability of sister is not selected is,
( 1 – 1 / 5 )
= 4 / 5.

So, required probability is,
p[( A and B not ) or ( B or not A )]
= ( 1 / 7 x 4 / 5 ) + ( 1 / 5 x 6 / 7 )
= 10 / 35
= 2 / 7.

Rough Workspace

Example #2
One speaker A tells truth in 75% cases and another speaker B in 80% of cases. What is the probability of cases are they likely to contradict each other, narrating the same incident?

1. 1 / 20
2. 3 / 20
3. 5 / 20
4. 7 / 20

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Answer: Option (D)
How to Solve
Let X = Event that A speaks the truth.
And, Y = Event that B speaks the truth.

Then, p(X) = 75%
= 75 / 100
= 3 / 4.

p(Y) = 80%
= 80 / 100
= 4 / 5.

A tells lie = ( 1 – 3 / 4 )
= 1 / 4.

B tells lie = (1 – 4 / 5 )
= 1 / 5.

So, p[( A speaks the truth and B tells a lie ) or ( A tells a lie and B speaks truth )]
= ( 3 / 4 x 1 / 5 ) + ( 1 / 4 x 4 / 5 )
= 3 / 20 + 1 / 5
= 7 / 20.

Rough Workspace

Example #3
In a simultaneous throw of two coins, what is the probability at lest one head?

1. 1 / 4
2. 2 / 4
3. 3 / 4
4. 4 / 4

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Answer: Option (C)
How to Solve
S = { HH, TT, HT, TH }

Let, E = event of getting at least one head.
= { TH, HH, HH }

p(E) = n(E) / n(S)
= 3 / 4.

Rough Workspace

Example #4
A positive integer is selected at a random and is divided by 9. What is the probability that the remainder is not 1?

1. 2 / 9
2. 5 / 9
3. 7 / 9
4. 8 / 9

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Answer: Option (D)
How to Solve
E( not 1 ) = { 0, 2, 3, 4, 5, 6, 7, 8 }
So, p(E) = 8 / 9.
Rough Workspace

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