Question

(i) Two-digit numbers are formed from the digits 2, 0, 5, 7 without repetition. Complete the following activity to find the probability that the numbers so formed are divisible (a) by 3 (b) by 5.

S={[

]}, n (5)

Event A : The numbers formed are divisible by 3.

A = {27, 57, 72, 75}

.. n(A): P(A) =

n(A)

n(S)

Event B : The numbers formed are divisible by 5.

B = {20, 25, 50, 70, 75}

... n(B) =,

P(B): n(B)

n(S)​

Answer 1

Answer:

S={20 , 25 , 27 , 52 , 50 , 57 , 72 , 70 , 75}

n (S) = 9

Event A : The numbers formed are divisible by 3.

A = {27, 57, 72, 75}

n(A)= 4

p(A) =n(A) / n(S)

p( A ) = 4 / 9

Event B : The numbers formed are divisible by 5.

B = {20, 25, 50, 70, 75}

n(B) = 5

p(B) = n(B) / n(S)

p( B ) = 5 / 9

Answer 2

Given:

two-digit numbers are formed from the digits 2,0,5,7 without repetition.

To Find:

P(A) and P(B)

Solution:

S = [20, 25, 27, 52, 50, 57, 72, 70, 75]

n[S] = 9

Event A = the numbers are divisible by 3

A = [27, 57, 72, 75]

n[A] = 4

p[A] = $\frac{n[A]}{n[S]}$

      = $\frac{4}{9}$

Event B = the numbers are divisible by 5

B = [20, 25, 50, 70, 75]

n[B] = 5

p[B] = $\frac{n[B]}{n[S]}$

      = $\frac{5}{9}$

So, p[B] : n[B] = 5: 5/9