Question

Two numbers are selected randomly from the set S = (1, 2, 3, 4.5.6.7.8.9. 10)
without replacement one by one. If the probability that minimum of the two numbers is
divisible by 3 or maximum of the two numbers is divisible by 4 is P then the value of 90
Pis​

Answer 1

P is 38

Step-by-step explanation:

1) Let

A be event such that Min(S) is divisible by 3.

B be event such that Max(S) is divisible by 4.

2) For A:

Possible arrangements : (3,a) where a is 4 to 10.

                                         (6,a) where a is 7 to 10.

                                         (9,a) where a is 10.

Total 12 combinations .

3) For B :

Possible arrangements : (b,4) where b is 1 to 3.

                                          (b,8) where b is 1 to 7.

Total combinations : 10

4)  For A and B :

Possible arrangements : (3,4) , (3,8) & (6,8).

Total combinations : 3

5) Now, We want

$P(A \cup B) = P(A) +P(B)-P(A \cap B)\\ \\= \frac{12}{^{10}C_2}+\frac{10}{^{10}C_2}-\frac{3}{^{10}C_2}\\ \\=\frac{38}{90}$

Hence, Value of 90P is 38

Answer 2

1) Let

A be event such that Min(S) is divisible by 3.

B be event such that Max(S) is divisible by 4.

2) For A:

Possible arrangements : (3,a) where a is 4 to 10.

(6,a) where a is 7 to 10.

(9,a) where a is 10.

Total 12 combinations .

3) For B :

Possible arrangements : (b,4) where b is 1 to 3.

(b,8) where b is 1 to 7.

Total combinations : 10

4) For A and B :

Possible arrangements : (3,4) , (3,8) & (6,8).

Total combinations : 3

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