First slide

Theorems of probability

Question

The probability that two randomly selected subsets of the set $\{1, 2, 3, 4, 5\}$ have exactly two elements in their intersection, is

Moderate

A

$\frac{65}{2^{7}}$
B

$\frac{65}{2^{8}}$
C

$\frac{35}{2^{7}}$
D

$\frac{135}{2^{9}}$

Solution

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

Suppose that A ,. B are any two subsets of S
For each element of S has four choices, it may belongs to A, or it may belongs to B, or it may belongs both A and B or it may does not belongs to both A and B
So total number of cases is 4⁵

Let two elements be selected in C(5,2) ways .
Remaining elements are 3. each element has choice, it may lie in A or in B or not in both A and B
hence, the total favorable cases to the event is C(5,2) 3³

$∴ P (E) = \frac{^{5} C_{2} \times 3^{3}}{4^{5}} = \frac{27 \times 5}{2^{9}} = \frac{135}{2^{9}}$

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