Sasi Math (Revised for 1024)

Scroll:Probability >> probability >> saq (4230)

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 formed with the two numbers turning up is divisible by 3.

Answer:_______________

Two rotten eggs are mixed with 15 good ones. One egg is chosen at random. what is the probability of choosing a rotten egg

Answer:_______________

A die is thrown twice. Find the probability of getting a total of 9.

Answer:_______________

A number is selected at random from integers 1 to 100. Find the probability that it is

(i) a perfect square (ii) not a perfect cube

A perfect square

Not a perfect cube

Answer:_______________

A bag contains 6 white balls numbered from 1 to 6 and 4 red balls numbered from 7 to 10. A ball is drawn at random. Find the probability of getting

(i) an even - numbered ball (ii) a white ball

An even - numbered ball

A white ball

Answer:_______________

Two coins are tossed together. What is the probability of getting at most one head

Answer:_______________

Two coins are tossed together. What is the probability of getting at most one tail

Answer:_______________

A ticket is drawn from a bag containig 100 tickets. The tickets are numbered from one to One Hundred . What is the probability of getting a ticket with a number divisible by 10.

Answer:_______________

Two dice are thrown together. Find the probability that two digit number formed with the two numbers turning up is divisible by 3.

Answer:_______________

10)

Three rotten eggs are mixed with 14 good ones. One egg is chosen at random. what is the probability of choosing a rotten egg

Answer:_______________

Two dice are thrown together. Find the probability that two digit number formed with the two numbers turning up is divisible by 3.

Answer: $\frac{1}{3}$

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 x6 = 36

Let A be the event of getting two digit number formed with the two numbers turning up is divisible by 3.

A = { (1,2),(1,5),(2,1),(2,4)

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

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

n(A) = 12

P(A) =	n(A)	=	12	=	1
	n(S)		36		3

Two rotten eggs are mixed with 15 good ones. One egg is chosen at random. what is the probability of choosing a rotten egg

Answer: $\frac{2}{17}$

SOLUTION 1 :

Given number of good eggs = 15

Number of rotten eggs = 2

Total number of eggs, n(S) = 15 + 2 = 17

Let A be the event of choosing a rotten egg = 17

P(A) =	n(A)	=	2	=	$\frac{2}{17}$
	n(S)		17

A die is thrown twice. Find the probability of getting a total of 9.

Answer: $\frac{1}{9}$

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 a sum 9.

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

n(A) = 4

Hence P(A) = $\frac{n(A)}{n(S)}$ = $\frac{4}{36}$ = $\frac{1}{9}$ .

A number is selected at random from integers 1 to 100. Find the probability that it is

(i) a perfect square (ii) not a perfect cube

A perfect square Answer: $\frac{1}{10}$

Not a perfect cube Answer: $\frac{24}{25}$

SOLUTION 1 :

Sample space, S = { 1, 2, 3, 4........ 100}

n(S) = 100

(i) Let A be the event of choosing a perfect square number.

A = { 1, 4, 9,16, 25, 36, 49, 64, 81, 100 }

n(A) = 10.

P(A) =	n(A)	=	10	=	$\frac{1}{10}$
	n(S)		100

(ii) Let B be the event of choosing a number, which is not a perfect cube.

Perfect cube numbers from 1 to 100 is C = { 1, 8, 27,64 }.

n(C) = 4

n(B) = n(S) - n(C)

n(B) = 100 - 4 = 96

P(A) =	n(B)	=	96	=	$\frac{24}{25}$
	n(S)		100

A bag contains 6 white balls numbered from 1 to 6 and 4 red balls numbered from 7 to 10. A ball is drawn at random. Find the probability of getting

(i) an even - numbered ball (ii) a white ball

An even - numbered ball Answer: $\frac{1}{2}$

A white ball Answer: $\frac{3}{5}$

SOLUTION 1 :

Ther are 6 white balls and + 4 red balls.

n(S) = 6 white balls + 4 red balls

= 10.

(i) Let A be the event of drawing an even-numbered ball.

Even numbered white balls = { 2, 4, 6 }

Even numbered red balls = { 8, 10 }

A = { 2, 4, 6, 8, 10 }

n(A) = 5.

P(A) =	n(A)	=	5	=	$\frac{1}{2}$
	n(S)		10

(ii) Let B be the event of drawing a white ball.

n(B) = 6

P(A) =	n(A)	=	6	=	$\frac{3}{5}$
	n(S)		10

Two coins are tossed together. What is the probability of getting at most one head

Answer: $\frac{3}{4}$

SOLUTION 1 :

Sample space S = {HH,HT,TH,TT}

n(S) = 4

Let A be the event of gettting atmost one head.

A = { HH,HT,TH}

n(A) = 3

P(A)	=	n(A)	=	$\frac{3}{4}$
		n(S)

Two coins are tossed together. What is the probability of getting at most one tail

Answer: $\frac{3}{4}$

SOLUTION 1 :

Sample space S = {HH,HT,TH,TT}

n(S) = 4

Let A be the event of gettting atmost one head.

A = { HT,TH,TT}

n(A) = 3

P(A)	=	n(A)	=	$\frac{3}{4}$
		n(S)

A ticket is drawn from a bag containig 100 tickets. The tickets are numbered from one to One Hundred . What is the probability of getting a ticket with a number divisible by 10.

Answer: $\frac{1}{10}$

SOLUTION 1 :

Here S = {1,2,3,4....100 }

n(S) = 100.

Let A be the event of choosing a ticket with a number divisible by 10

A = { 10,20,30,40,50,60,70,80,90,100 }

n(A) = 10

P(A) =	n(A)	=		10	=	1	= $\frac{1}{10}$
	n(S)			100		10

Two dice are thrown together. Find the probability that two digit number formed with the two numbers turning up is divisible by 3.

Answer: $\frac{1}{3}$

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 x6 = 36

Let A be the event of getting two digit number formed with the two numbers turning up is divisible by 3.

A = { (1,2),(1,5),(2,1),(2,4)

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

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

n(A) = 12

P(A) =	n(A)	=	12	=	1
	n(S)		36		3

10)

Three rotten eggs are mixed with 14 good ones. One egg is chosen at random. what is the probability of choosing a rotten egg

Answer: $\frac{3}{17}$

SOLUTION 1 :

Given number of good eggs = 14

Number of rotten eggs = 3

Total number of eggs, n(S) = 14 + 3 = 17

Let A be the event of choosing a rotten egg = 17

P(A) =	n(A)	=	3	=	$\frac{3}{17}$
	n(S)		17