# The probability that a person will travel by plane is 3/5 and that he will travel by trains is 1/4. What is the probability that he (she) will travel by plane or train? - Mathematics

The probability that a person will travel by plane is 3/5 and that he will travel by trains is 1/4. What is the probability that he (she) will travel by plane or train?

#### Solution

We have two events such that
A = a person will travel by plane
and B = a person will travel by train.
i.e.

$P\left( A \right) = \frac{3}{5}$  and $P\left( B \right) = \frac{1}{4}$
Since A and B are mutually exclusive events, we have:
P (A ∩ B) = 0
By addition theorem, we have:
P (A ∪ B) = P(A) + P (B) - P (A ∩ B)
=  $\frac{3}{5} + \frac{1}{4} - 0 = \frac{12 + 5}{20} = \frac{17}{20}$
Hence, required probability = $\frac{17}{20}$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 33 Probability
Exercise 33.4 | Q 19 | Page 68