First slide

Theorems of probability

Question

Of all the mappings that can be defined from the set A : {1,2,3, 4} $\to$ B : {5, 6,7 ,8, 9} , a mapping is randomly
selected. The chance that the selected mapping is strictly monotonic is

Moderate

A

$\frac{1}{125}$
B

$\frac{2}{125}$
C

$\frac{3}{25}$
D

$\frac{4}{25}$

Solution

Each pre-image in set A can be assigned any one of the 5 images from set B
Hence total number of functions are $n (S) = 5^{4} = 625$
For strictly monotonic function either function is increasing or decreasing.
For which four different images are used, which can be selected $^{5} C_{4}$ way.
Hence number of monotonic functions are $n (A) = 2 \cdot^{5} C_{4} = 10$ (either increasing or decreasing)
$∴ P (A) = \frac{10}{625} = \frac{2}{125}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App