Tips And Tricks And Shortcuts For Probability Questions

Tips and Tricks and Shortcuts for Probability

The Event which is likely to occur, measured by the ratio of the Favourable cases to the whole number of cases possible , known as Probability. In this Page Tips and Tricks for Probability is given.

Tips for Probability

Probability is a measure of the likelihood of an event occurring, which is determined by the ratio of favorable outcomes to the total number of possible outcomes.

The formula for calculating probability is:

P(E) = $\frac{Number of Favorable Outcomes}{Total Number of Possible Outcomes}$

• In mathematical terms,
Probability represents the ratio of desired outcomes to the total number of possible outcomes.
• When solving probability questions, if it is easier to find the probability of an event not happening, you can calculate that probability and subtract it from 1.
• When encountering the term “or” in a question,
Use addition (+) when applying the Fundamental Principle of Counting to solve the problem.
• When encountering the term “and” in a question,
Use multiplication (x) when applying the Fundamental Principle of Counting to solve the problem.

Tips and Tricks for Probability Questions and their solution

Question 1.  A die is rolled, find the probability that an even number is obtained ?

Options

(a) $\frac{3}{4}$

(b) $\frac{1}{2}$

(c) $\frac{1}{4}$

(d) None of these

Solutions    Let us first write the sample space, S of the experiment.

S={1,2,3,4,5,6}

Let E be the event “an even number is obtained” and write down.

E= {2,4,6}

We can use the formula of the classical probability.

P(E)= $\frac{n(E)}{n(S)}$ = $\frac{3}{6}$ =$\frac{1}{2}$.

Correct Options (b)

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Question 2. Two coins are tossed, find the probability that two heads are obtained.  Note: Each coin has two possible outcomes H (heads) and T (Tails).

Options

(a) $\frac{1}{4}$

(b) $\frac{1}{2}$

(c) $\frac{3}{2}$

(d) None of these

Solutions    The sample space S is given by.

S = {(H,T),(H,H),(T,H),(T,T)}

Let E be the event “two heads are obtained”.
E = {(H,H)}

We use the formula of the classical probability.

P(E) =$\frac{n(E)}{n(S)}$ = $\frac{1}{4}$

Correct Options (a)

Question 3. Two dice are rolled, find the probability that the sum is

a) equal to 1

b) equal to 4

c) less than 13

Solution      The sample space S of two dice is shown below.

S = {(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)

(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)

(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)

(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)

(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)

(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}

a)  Let E be the event “sum equal to 1”. There are no outcomes which correspond to a sum equal to 1, hence

P(E) = $\frac{n(E)}{n(S)}$ = $\frac{0}{36}$ = 0

Quickest Way : Sum is always greater than or equal to 1 . So it is Impossible Event means Probability will be 0.

b) Three possible outcomes give a sum equal to 4: E = {(1,3),(2,2),(3,1)}, hence.

P(E) = $\frac{n(E)}{n(S)}$ = $\frac{3}{36}$ = $\frac{1}{12}$

c) All possible outcomes, E = S, give a sum less than 13, hence.

P(E) = $\frac{n(E)}{n(S)}$ = $\frac{36}{36}$ = 1

Quickest Way : Sum is always less than 13 . So it is sure Event means Probability will be 1.

Question 4. A Speak truth truth in 20 % of cases and B in 40 % of  cases. In what Percentages of cases are they likely to Contradict to each other in

Narrating the Same Event?

Options

(a) 40 %

(b) 44 %

(c) 42 %

(d) None of these

Solutions    They contradict each other if one of them Speaks and the other one lies. and vice – versa.

Required Percentages = 0.20 x (1 – 0.40 ) + (1- 0.20) x 0.40 = 0.44 = 44 %

Correct Option (b)

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2 comments on “Tips And Tricks And Shortcuts For Probability Questions”

• Livi

Thanks for your tips and tricks

• Atchaya

It’s very useful for me to solve probability related sums