Probability CBSE HOTS questions(KVS Bank)

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20 Mar 2009 10:25:12 IST

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20 Mar 2009 10:25:12 IST

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Probability CBSE HOTS questions(KVS Bank)

Mathematics , Statistics

Chapter 9 PROBABILITY

1 Mark Questions

If A and B are two independent events, find P(B) when P(A U B ) = 0.60 and P(A) = 0.35.

A card is drawn from a well shuffled pack of 52 cards. The outcome is noted and the pack is again reshuffled without replacing the card. Another card is then drawn. What is the probability that the first card is a spade and the second is a Black King.

Find the chance of drawing two white balls in succession from a bag containing 3 red and 5 white balls, the ball first drawn not replaced.

Given P(A) = 1/4, P(B) = 2/3 and P(A U B ) = 3/4. Are the events independent ?

Given P(A) = 0.3, P(B) = 0.2. find P(B/A) if A and B are mutually exclusive events.

Does the following table represents a probability distribution ?

X	-2	-1	0	1	2
P(X)	0.1	0.2	-0.2	0.4	0.5

Father, mother and son line up at random for a family picture. If E is the event “Son on one end” and F is the event “Father in middle”, Find P(F/E).

A bag contains 5 brown and 4 white socks. A man pulls out 2 socks. Find the probability that these socks are of same colour.

Q10

Out of 30 consecutive integers, 2 are chosen at random. Find the probability that their sum is odd.

Q11

An urn contains 9 balls,two of which are red, 3 blue and 4 black. Three balls are drawn at random. Find the probability that they are of the same color.

Q12

If X is a random variable with probability distribution as given below, find the value of k.

X	0	1	2	3
P(X)	k	3k	3k	k

Q13

A random variable X takes the values 0,1,2,3 and its mean is 1.3. If P(X =3)= 2P(X = 1) and P(X =2)= 0.3. then find P(X = 0).

Q14

If P(A ) = 7/13, P(B) = 9/13 and P(A B) = 4/13. Find P(A’/B).

Q15

A couple has 2 children. Find the probability that both the children are boys, if it is known that at least one of the children is a boy.

Q16

A coin is tossed 7 times. Write the probability distribution of getting r heads.

Q17

If P(A )=0.4, P(B)= p and P(A U B)= 0.7, find the value of p if A and B are independent events.

Q18

In two successive throws a pair of dice, find the probability of getting a total of 8 each time

Q19

A policeman fires 4 bullets on a dacoit. The probability that the dacoit will not be killed by a bullet is 0.4. What is the probability that the dacoit is still alive ?

Q20

4 Cards are drawn from a well shuffled pack of 52 cards. Find the probability of drawing all the 4 cards of the same suit if a card is replaced after each other.

4 Mark Questions

‘A’ speaks truth in 60% cases and ‘B’ in 90% cases. In what % of cases are they likely to contradict each other in stating the same fact?

The probability of student A passing an examination is 3/5 and of student B passing is 4/5. Assuming the two events : ’A passes’, ‘B passes’, as independent find the probability of:

a. Both students passing the examination

b. Only A passing the examination

c. Only one of the two passing the examination

d. Neither of the two passing the examination

A problem in Mathematics is given to three students whose chances of solving it are 1/3,1/5,1/6. What is the probability that at least one of them solves the problem.

A’ speaks truth in 60% cases and ‘B’ in 90% cases. In what % of cases are they likely to contradict each other in stating the same fact?

A and B are two independent events. The probability that both A and B occur is 1/6 and the probability that neither of them occurs is 1/3. Find the probability of occurrence of A.

A coin is tossed until a head appears or until it has been tossed three times. Given that ‘head’ does not occur on the first toss, what is the probability that the coin is tossed thrice?

A company has two plants to manufacture scooters. Plant-1 manufactures 70% of the scooters and Plant-2 manufactures 30%. At Plant-1, 80% of the scooters are rated of standard quality and at Plant-2, 90% of the scooters are rated of standard quality. A scooter is chosen at random and is found to be of standard quality. Find the probability that it has come from Plant-2.

Find the mean and standard deviation of the probability distribution of the numbers obtained when a card is drawn at random from a set of 7 cards numbered 1 to 7.

A pair of dice is rolled twice. Let X denote the number of times, ‘ a total of 9 is obtained’. Find the mean and variance of the random variable X.

Q10

A box contains 12 bulbs of which 3 are defective. A sample of 3 bulbs is selected from the box. Let X denote the number of defective bulbs in the sample, find the probability distribution of X.

Q11

A box contains 12 bulbs of which 3 are defective. A sample of 3 bulbs is selected from the box. Let X denote the number of defective bulbs in the sample, find the probability distribution of X.

Q12

Two dice are thrown six times. ‘A total of 7’ is considered as success. Find the probability of at least 4 successes.

Q13

Four cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that

i. All the four cards are spades?

ii. Only three cards are spades?

iii. None is a spade?

Q14

The sum of mean and variance of a binomial distribution is 35/16, for 5 trials. Find the distribution.

Q15

A man takes a step forward with probability 0.4 and backwards with probability 0.6. Find the probability that at the end of eleven steps he is one step away from the starting point.

Q16

10% of the tools produced by a machine are defective. Find the probability distribution of the number of defective tools in a sample of 3 drawn at random.

Q17

3 defective bulbs are mixed with 7 good ones, 3 bulbs are drawn at random. Find the probability distribution of the defective bulbs.

Q18

The probability distribution of a random variable X is given by

X	0	1	2
P(X)	3c³	4c-10c²	5c - 1

where c > 1 then find each of the following :

i. c

ii. P(X< 2)

iii. P(1 < X≤2)

Q19

A letter is known have to come from TATANAGAR or CALCUTTA. On the envelope just two consecutive letters TA are visible. Find the probability that the letter has come from

i. Calcutta

ii. Tatanagar

Q20

Fatima and John appear in an interview for two vacancies on the same post. The probability of Fatima’s selection is 1/7 and that of John’s selection is 1/5. What is the probability that:

i. Both of them will be selected.

ii. Only one of them is selected.

iii. None of them will be selected.

6 Mark Questions

A pair of dice is thrown 7 times . If getting a total of 7 is considered a successes, what is the probability of

I) No Success II) 6 Success III) At least 6 Success IV) At most 6 Successes.

Let X denote the number of hours you study during a randomly selected school day. The probability that X can take the value x has the following form where k is some unknown constant:

P(X=x) = {0.1 if x= 0

kx if x =1 or 2

k(5-x) if x =3 or 4

0,otherwise }

(a) Find the value of k

(b) What is the probability that you study

(i) At least 2 hours ?

(ii) Exactly two hours ?

(iii) At most two hours ?

Three urns contain respectively 3 green and 2 white balls , 5green and 6 white balls and 2 green, 4white balls. One ball in drawn from each urn. Find the mean and variance of the probability distribution of the discrete random variable ,”Number of white balls drawn”.

A pack of playing cards was found to contain only 51 cards. If the first 13 cards which are examined are all red, what is the probability that the missing card is black.

Answers PROBABILITY

1 Mark Questions

1) 5/13

25/2652

5/14

Yes

1/2

48/108

15/29

Q10

11/16

Q11

5/84

Q12

1/8

Q13

0.4

Q14

5/9

Q15

1/3

Q16

P(r)=⁷c_r(1/2)⁷, r=0,1,2....7

Q17

0.5

Q18

25/1296

Q19

0.0256

Q20

1/64

4 Mark Questions

1) 5 2/77

2) 1 2/25,3/25,11/25,

2/25

3) 5/9

4) 42%

½ OR 1/3

1/2

27/83

4,2

2/9,16/81

Q10

X	0	1	2	3
P(x)	84/220	108/220	27/220	1/220

Q11

X	0	1	2
P(x)	9/16	3/8	1/16

Q12

(406/6⁶)

Q13

1/256, 3/64, 81/256

Q14

(3/4+1/4)⁵

Q15

¹¹C₅(3/5)⁵(2/5)⁵

Q16

X	0	1	2	3
P(x)	727/1000	243/1000	27/1000	1/1000

Q17

X	0	1	2	3
P(x)	7/24	21/40	7/40	1/120

Q18

1/3, 1/3, 2/3

Q19

4/11

Q20

1/35, 2/7, 24/35

6 Mark Questions

¹⁾( 5/6)⁷,35(1/6)⁷,(1/6)⁵,1-(1/6)⁷

2) ( a) 0.15 (b) 0.75 ,0.3,0.55

3) 532/330,0.71

4) 2/3

P(x)

625/1296

500/1296

150/1296

20/1296

1/1296

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Comments (3)

Bhaskar Tetarbe

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Joined: 15 Jul 2007 13:04:19 IST

Posts: 245

20 Mar 2009 19:57:56 IST

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My source - KV question bank

Sunny Shah

Hot goIITian

Joined: 8 Nov 2007 19:28:28 IST

Posts: 166

20 Mar 2009 20:37:26 IST

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This may sound cheap....but deres a mistake in d question numbering...lolz..

jithmeister

Scorching goIITian

Joined: 5 Jun 2008 20:37:54 IST

Posts: 271

20 Mar 2009 22:36:45 IST

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Wow.... can u link to any other KVS question articles/forums ? I guess its too late now but again...pls post the link if u have.. PLS

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Chapter 9 PROBABILITY

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