Probability Test

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Probability Test - 5

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Weekly Quiz Competition

Question 1
1 / -0

In a simultaneous roll of two dice, the probability of getting a total of 7 is

A

B

C

D

Solution

Total number of possible outcomes = (6)² = 36
Favourable cases = (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) = 6
Required probability = = .
Question 2
1 / -0

If a fair coin is tossed twice, what is the probability of getting heads in both the trials?

A

B

C

D
1

Solution

Required probability = =
Hence, answer option 1 is correct.
Question 3
1 / -0

Tickets numbered from 1 to 25 are mixed up together and a ticket is drawn at random. What is the probability that the ticket drawn contains a prime number?

A

B

C

D

Solution

Favourable cases = 2, 3, 5, 7, 11, 13, 17, 19, 23 = 9 cases
Total number of cases = 25
Hence, probability = ^.
Question 4
1 / -0

The probability that a card drawn from a pack of 52 cards will be either a diamond or a king is

A

B

C

D

Solution

Total ways of drawing a card = 52
There are 13 diamond and 4 kings, out of which there is one king of diamond.
Number of favourable ways = (13 + 4 - 1) = 16
Required probability = ^{Hence, answer option 3 is correct.}
Question 5
1 / -0

The probability that a leap year selected at random will contain 53 Sundays is

A

B

C

D

Solution

Leap years have 366 days.
366/7 = 52, remainder = 2
52 weeks are there = 52 Sundays + 2 days extra
The 2 extra days can be Sunday and Monday, Monday and Tuesday, Tuesday and Wednesday, Wednesday and Thursday, Thursday and Friday, Friday and Saturday or Saturday and Sunday.
Thus, we have 7 possible combinations of which 2 combinations have a Sunday.
Thus, the required probability is 2/7.
Hence, answer option 2 is correct.
Question 6
1 / -0

A card is drawn from a well-shuffled pack of 52 cards. The probability of getting a queen of club or king of heart is

A

B

C

D
none of these

Solution

Required probability = = Hence, answer option 3 is correct.
Question 7
1 / -0

A bag contains 6 black, 9 white and 5 red balls. Three balls are drawn at random. What is the probability that all the balls drawn are black?

A

B

C

D
None of these

Solution

Probability of drawing three black balls =
Question 8
1 / -0

A card is drawn at random from a pack of 52 cards. The probability of getting a red card or an ace is

A

B

C

D

Solution

Total number of ways to draw a card = 52
Total favourable cases = 26( Red Card ) + 4( Ace Card ) - 2( Red Ace Card ) = 28

Probability = Hence, answer option 4 is correct.
Question 9
1 / -0

A bag contains 8 white and 5 red balls. Three balls are drawn at random. What is the probability that all the balls drawn are white?

A

B

C

D
None of these

Solution

Required probability = =
Question 10
1 / -0

A pair of dice is thrown and the numbers appearing have a sum greater than or equal to 10. The probability of getting a sum of 11 is

A

B

C

D

Solution

Total number of possible cases = (4, 6) (5, 5) (6, 4) (6, 6) (5, 6) (6, 5) = 6
Favourable events = 2
Required Probability =
Hence, answer option 4 is correct.
Question 11
1 / -0

A bag contains 9 red and 6 white balls. 3 balls are drawn at random. What is the probability that 1 ball is red and the other 2 are white?

A

B

C

D
None of these

Solution

1 red ball can be drawn in ⁹C₁ = 9 ways
2 white balls can be drawn in ⁶C₂= = 15 ways
Thus, probability of drawing 1 red and 2 white balls =
Hence, answer option 1 is correct.
Question 12
1 / -0

Tickets numbered from 1 to 20 are mixed up together and then a ticket is drawn at random. What is the probability that the drawn ticket has a number which is a multiple of either 3 or 5?

A

B

C

D
None of these

Solution

Total cases = 20
Favourable cases = (3, 5, 6, 9, 10, 12, 15, 18, 20) i.e. 9 cases
Probability = 9/20
Hence, answer option 1 is correct.
Question 13
1 / -0

In a lottery of 50 tickets numbered 1 to 50, 2 tickets are drawn simultaneously. The probability that both the tickets drawn have prime numbers is

A

B

C

D

Solution

Prime numbers from 1 to 50 = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 = 15 (total)
Required probability = = = = = ^{Hence, answer option 2 is correct.}
Question 14
1 / -0

A box contains 15 electric bulbs, out of which 3 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective is

A

B

C

D
none of these

Solution

Cases of non-defective bulbs = ¹²C₂ = 66
Total cases = ¹⁵C₂ = 105
Total cases when there is at least 1 defective bulb = 105 - 66 = 39
Probability that at least 1 is defective = = Hence, answer option 2 is correct.
Question 15
1 / -0

3 dice are rolled together. The probability of getting a total of at least 6 is

A

B

C

D
None of these

Solution

Total number of possible outcomes = 6³ = 216
Number of cases of getting at least 6 = Total number of cases - Number of cases of getting at most 5
Number of cases of getting at most 5 = (1, 1, 1) (1, 2, 1) (1, 1, 2) (2, 1, 1) (2, 2, 1) (1, 2, 2,)
(2, 1, 2) (3, 1, 1,) (1, 3, 1) (1, 1, 3)
= 10 cases
Thus, required probability = = =
Hence, answer option 2 is correct.
Question 16
1 / -0

A natural number is chosen at random from the first 100. The probability of it being divisible by 3 or 5 is

A

B

C

D

Solution

There are 33 numbers in the first 100 natural numbers that are divisible by 3.
There are 20 numbers in the first 100 natural numbers that are divisible by 5.
P (A) = Probability divided by 3 =
P (B) = Probability divided by 5 =
P (A B) = Probability divided by both 3 and 5 =
P (A B) = P(A) + P (B) - P (A B)
=
=
Hence, answer option 4 is correct.
Question 17
1 / -0

4 cards are drawn at random from a pack of 52 cards. The probability of getting all the 4 cards of the same number or face is

A

B

C

D
None of these

Solution

First card can be drawn from the pack in 52 ways.

Second card can be drawn in 51 ways.

Third card can be drawn in 50 ways.

Fourth card can be drawn in 49 ways.

So total number of ways in which 4 cards can be drawn from a pack of 52 cards =

Now these 4 cards are drawn one after another so we have to make this draw an favourable event such that the order of cards does not change the outcome.

Hence for 4 cards the total number of ways in which these can be ordered =

So total number of outcomes :

= 270725

Now we need to find the outcomes where 4 cards are of same numbers or face value:

Let E = {(1, 1, 1, 1), (2, 2, 2, 2), â¦â¦., (K, K, K, K)} = 13
Required probability = ^{Hence, answer option 1 is correct.}
Question 18
1 / -0

Let A and B be two independent events. The probability that both A and B occur is and the probability that neither A nor B occurs is . The respective probabilities of A and B are

A
and

B
and

C
and or and

D
None of these

Solution

P(A) = x
P(B) = y
P (A B) =
P (Neither A nor B) =
i.e. P( A B ) =
And, P(A) + P (B) = P (A U B ) + P (A B) =
From the options,
x =, y = or x = , y = as for both x + y =^{Also, as A and B are independent, xy = 1/30
Hence, answer option 3 is correct.}
Question 19
1 / -0

In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys will be selected is

A

B

C

D

E
None of these

Solution

Required probability = = = ^{Hence, answer option 3 is correct.}
Question 20
1 / -0

An unbiased dice is rolled three times. The probability that the minimum number on any toss is not less than 3 and maximum not greater than 5 is

A

B

C

D

Solution

Favourable case is that the number appearing on the die is 3, 4 or 5, the probability of the occurrence of which is =
Thus, the required probability when the die is rolled thrice is =
Hence, answer option 1 is correct.