Probability - online MCQ test 1

Question 1: 10 cards are picked out of order and shuffled further. The cards are: 9,5,4,2,6,8,2,3,7,8. What is the probability of picking a card which is more than 5?

A) 1/2

B) 4/3

C) 1/4

D) None

Explanation:
Total number of cards = 10
Total cards having value more than 5 = 5
i.e. {6, 9, 7, 6, 8}
Total cards having an even number = 6

i.e. {6, 6, 4, 2, 8, 2}
So, the probability of picking a card has a value of more than 5 = 5/10 = 1/2.

Question 2: Compute the probability of the occurrence of an event if the probability the event not occurring is 0.56?

A) 0.33

B) 0.35

C) 0.40

D) 0.44

Explanation:
P(not E) = 0.56
We know that,
P(E) + P(not E) = 1
So, P(E) = 1 – P(not E)
P(E) = 1 – 0.56
Or, P(E) = 0.44

Question 3: A bag containing red and blue balls, the probability of picking a red ball is x/2. What is the value of “x” if the probability of picking a blue ball is ⅔.

A) 1/4

B) 2/3

C) 2/5

D) 1/2

Explanation:
P(picking a red ball) + P(picking a blue ball) = 1
x/2 + ⅔ = 1
=> 3x + 4 = 6
=> 3x = 2
Or, x = ⅔

Question 4: Two cards are drawn at random and without replacement from a pack of 52 playing cards. What would be the probability that both the cards are black.

A) 24/102

B) 25/102

C) 3/7

D) 1/2

Explanation:
Let  P1= the probability of getting  first  black card  and P2= the probability of getting a black card on the second draw.
P1=26/52
P2=25/51
The probability that both the cards are black
=P1*P2=(26/52)*(25/51)=25/102

Question 5: A bag contains 7 white, 3 red and 4 black balls. A ball drawn at random. What is the the probability that it is a red or a black ball?

A) 1/4

B) 7/12

C) 1/3

D) 1/2

Explanation: .
Total balls =5+3+4=12 .
Red and black ball = 7 .
Therefore, the probability of getting one ball either red or black =7/12

Question 6: A bag contains 7 white, 3 red and 4 black balls. A ball drawn at random. What is the probability that not drawing a red ball ?

A) 3/14

B) 11/14

C) 10/24

D) None

Explanation:
The probability of getting  red ball would be 3/14.
Therefore, The probability of not getting  a  red ball would be (1-3/14)=11/14.

Question 7: A bag contains 6 red balls, 8 white balls, 5 green balls and 3 black balls. One ball is drawn at random from the bag. Find the probability that the ball drawn is neither white nor black ?

A) 1/5

B) 2/5

C) 1/2

D) 1/3

Explanation: The probability of drawing neither white nor black ball would be 11/ 22

Question 8: A die is thrown once. What is the probability that the number is greater than 2?

A) 1/5

B) 2/3

C) 3/7

D) 1/2

Explanation: Total number on die having value more than 2 = 4
i.e. {3, 4, 5, 6}
The probability that the number is greater than 2 =4/6=2/3

Question 9: If two coins are thrown in the air then the probability of getting two heads is :?

A) 1/4

B) 7/8

C) 3/7

D) 1/2

Explanation:
Total outcomes when two coins are thrown simultaneously are (HH),(TT),(TH),(HT)
Two heads are (HH) i.e 1
P(2 heads ) = number of  two heads /total outcomes = 1/4

Question 10: If a card is drawn from a dec of a 52 cards then the probability of getting a red card is:?

A) 4/13

B) 2/5

C) 9/13

D) 1/2

Explanation:
The total number of cards are 52
The number of red cards are = 13
diamonds + 13 heart = 26
P(red card) = no. of red cards/total number of cards = 26/52 = 1/2

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