Sasi Math (Revised for 1024)

Scroll:Probability >> probability >> ps (4489)

Written Instructions:

For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..

For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.

Leave your answers in the simplest form or correct to two decimal places.

Two dice are thrown together. Find the probability that two digit number with the two numbers turning up is divisible by 5.

Answer:_______________

Two dice are thrown together. Find the probability that two digit number with the two numbers turning up is divisible by 10.

Answer:_______________

Two dice are thrown together. Find the probability that two digit number with the two numbers turning up is divisible by 4.

Answer:_______________

Two dice are thrown together. Find the probability that two digit number with the two numbers turning up is divisible by 9.

Answer:_______________

Two dice are thrown together. Find the probability that two digit number with the two numbers turning up is divisible by 6.

Answer:_______________

Two dice are thrown together. Find the probability that two digit number with the two numbers turning up is divisible by 12.

Answer:_______________

Two dice are thrown together. Find the probability that two digit number with the two numbers turning up is divisible by 8.

Answer:_______________

Two dice are thrown together. Find the probability that two digit number with the two numbers turning up is divisible by 11.

Answer:_______________

Two dice are thrown together. Find the probability that two digit number with the two numbers turning up is divisible by 7.

Answer:_______________

10)

Two dice are thrown together. Find the probability that two digit number with the two numbers turning up is divisible by 2.

Answer:_______________

Two dice are thrown together. Find the probability that two digit number with the two numbers turning up is divisible by 5.

Answer: $\frac{7}{36}$

SOLUTION 1 :

When two dice are thrown, the sample space is

S = { (1,1), (1,2), (1,3), (1,4), (1,5), (1,6),

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6),

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6),

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6),

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6),

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6) }

n (S) = 6 x 6 = 36.

Let A be the event of getting two digit number formed with the two numbers turning up is divisible by 5

A = { (1,4) ,(2,3), (3,2), (4,1), (4,6), (5,5), (6,4) }

n(A) = 7.

Hence P(A) = $\frac{n(A)}{n(S)}$

= $\frac{7}{36}$

Two dice are thrown together. Find the probability that two digit number with the two numbers turning up is divisible by 10.

Answer: $\frac{1}{12}$

SOLUTION 1 :

When two dice are thrown, the sample space is

S = { (1,1), (1,2), (1,3), (1,4), (1,5), (1,6),

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6),

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6),

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6),

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6),

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6) }

n (S) = 6 x 6 = 36.

Let A be the event of getting two digit number formed with the two numbers turning up is divisible by 10

A = { (4,6), (5,5), (6,4) }

n(A) = 3.

Hence P(A) = $\frac{n(A)}{n(S)}$

= $\frac{3}{36}$ = $\frac{1}{12}$

Two dice are thrown together. Find the probability that two digit number with the two numbers turning up is divisible by 4.

Answer: $\frac{1}{2}$

SOLUTION 1 :

When two dice are thrown, the sample space is

S = { (1,1), (1,2), (1,3), (1,4), (1,5), (1,6),

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6),

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6),

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6),

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6),

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6) }

n (S) = 6 x 6 = 36.

Let A be the event of getting two digit number formed with the two numbers turning up is divisible by 4

A = { (1,3) ,(2,2), (2,6), (3,1), (3,5), (4,4), (5,3), (6,2), (6,6) }

n(A) = 9

Hence P(A) = $\frac{n(A)}{n(S)}$

= $\frac{9}{36}$ = $\frac{1}{4}$

Two dice are thrown together. Find the probability that two digit number with the two numbers turning up is divisible by 9.

Answer: $\frac{5}{36}$

SOLUTION 1 :

When two dice are thrown, the sample space is

S = { (1,1), (1,2), (1,3), (1,4), (1,5), (1,6),

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6),

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6),

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6),

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6),

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6) }

n (S) = 6 x 6 = 36.

Let A be the event of getting two digit number formed with the two numbers turning up is divisible by 9

A = { (3,6), (4,5), (5,4), (6,3) }

n(A) = 4.

Hence P(A) = $\frac{n(A)}{n(S)}$

= $\frac{4}{36}$ = $\frac{1}{9}$

Two dice are thrown together. Find the probability that two digit number with the two numbers turning up is divisible by 6.

Answer: $\frac{1}{6}$

SOLUTION 1 :

When two dice are thrown, the sample space is

S = { (1,1), (1,2), (1,3), (1,4), (1,5), (1,6),

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6),

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6),

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6),

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6),

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6) }

n (S) = 6 x 6 = 36.

Let A be the event of getting two digit number formed with the two numbers turning up is divisible by 6

A = { (1,5) ,(2,4), (3,3), (4,2), (5,1), (6,6) }

n(A) = 6.

Hence P(A) = $\frac{n(A)}{n(S)}$

= $\frac{6}{36}$ = $\frac{1}{6}$

Two dice are thrown together. Find the probability that two digit number with the two numbers turning up is divisible by 12.

Answer: $\frac{1}{36}$

SOLUTION 1 :

When two dice are thrown, the sample space is

S = { (1,1), (1,2), (1,3), (1,4), (1,5), (1,6),

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6),

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6),

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6),

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6),

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6) }

n (S) = 6 x 6 = 36.

Let A be the event of getting two digit number formed with the two numbers turning up is divisible by 12

A = { (6,6) }

n(A) = 3.

Hence P(A) = $\frac{n(A)}{n(S)}$

= $\frac{1}{36}$

Two dice are thrown together. Find the probability that two digit number with the two numbers turning up is divisible by 8.

Answer: $\frac{5}{36}$

SOLUTION 1 :

When two dice are thrown, the sample space is

S = { (1,1), (1,2), (1,3), (1,4), (1,5), (1,6),

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6),

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6),

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6),

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6),

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6) }

n (S) = 6 x 6 = 36.

Let A be the event of getting two digit number formed with the two numbers turning up is divisible by 8

A = { (2,6), (3,5), (4,4), (5,3), (6,2) }

n(A) = 5.

Hence P(A) = $\frac{n(A)}{n(S)}$

= $\frac{5}{36}$

Two dice are thrown together. Find the probability that two digit number with the two numbers turning up is divisible by 11.

Answer: $\frac{1}{18}$

SOLUTION 1 :

When two dice are thrown, the sample space is

S = { (1,1), (1,2), (1,3), (1,4), (1,5), (1,6),

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6),

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6),

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6),

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6),

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6) }

n (S) = 6 x 6 = 36.

Let A be the event of getting two digit number formed with the two numbers turning up is divisible by 11

A = { (5,6), (6,5) }

n(A) = 2.

Hence P(A) = $\frac{n(A)}{n(S)}$

= $\frac{2}{36}$ = $\frac{1}{18}$

Two dice are thrown together. Find the probability that two digit number with the two numbers turning up is divisible by 7.

Answer: $\frac{1}{6}$

SOLUTION 1 :

When two dice are thrown, the sample space is

S = { (1,1), (1,2), (1,3), (1,4), (1,5), (1,6),

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6),

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6),

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6),

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6),

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6) }

n (S) = 6 x 6 = 36.

Let A be the event of getting two digit number formed with the two numbers turning up is divisible by 7

A = { (1,6) ,(2,5), (3,4), (4,3), (5,2), (6,1) }

n(A) = 6.

Hence P(A) = $\frac{n(A)}{n(S)}$

= $\frac{6}{36}$ = $\frac{1}{6}$

10)

Two dice are thrown together. Find the probability that two digit number with the two numbers turning up is divisible by 2.

Answer: $\frac{1}{2}$

SOLUTION 1 :

When two dice are thrown, the sample space is

S = { (1,1), (1,2), (1,3), (1,4), (1,5), (1,6),

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6),

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6),

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6),

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6),

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6) }

n (S) = 6 x 6 = 36.

Let A be the event of getting two digit number formed with the two numbers turning up is divisible by 2

A = { (1,1}. (1,3), (1,5),

(2,2), (2,4), (2,6),

(3,1), (3,3), (3,5),

(4,2), (4,4), (4,6)

(5,1), (5,3), (5,5),

(6,2), (6,4), (6,6) }

n(A) = 18

Hence P(A) = $\frac{n(A)}{n(S)}$

= $\frac{18}{36}$ = $\frac{1}{2}$ .