AMCAT Previous Years Questions on Probablity



Topics
Sub- Topics
Expected Ques
Basic Mathematics
       6 – 8 Questions
Applied Mathematics
      8 – 10 Questions
Engineering Mathematics
       8 – 10 Questions

Question 1
The probability of getting heads in both trials when a balanced coin is tossed twice will be?
A. 1/4
B. 1/2
C. 1
D. 3/4

Correct Op: A
Probability of getting head in one trail = 1/2 ∴ Reqd Probability of getting heads in both the trails = 1/2 x 1/2 = 1/4
 
Question 2
A card is drawn from a well-shuffled pack of cards. The probability of getting a queen of club or king of the heart is?
A. 1/52
B. 1/26
C. 1/13
D. None of these

Correct Op: B
Total ways = 52 There is one queen of club and one king of heart favourable ways = 1 + 1 = 2. ∴ Required probability = 2/52 = 1/26
 
Question 3
If the probability that A will live 15 yr is 7/8 and that B will live 15 yr is 9/10, then what is the probability that both will live after 15 yr ?
A. 1/20
B. 63/80
C. 1/5
D. None of these

Correct Op: B
Required probability = P(A) x P(B) = (7/8) x (9/10) = 63/80
 
Question 4
The probability of drawing a red card from a deck of playing cards is
A. 2/18
B. 1/13
C. 1/4
D. 1/2

Correct Op: D
Total number of cards n(S) = 52 Number of red cards n(E) = 26 ∴ P(E) = n(E)/n(S) = 26/52 = 1/2
 
Question 5
When two dice are rolled, what is the probability that the sum of the numbers appeared on them is 11?
A. 1/6
B. 1/18
C. 1/9
D. 1

Correct Op: B
n(S) = 36 n(E) = {(5,6), (6,5)} = 2 ∴ p(E) = n(E) / n(S) = 2/36 = 1/18
 
Question 6
A bag contains 8 red and 5 white balls. 2 balls are drawn at random. What is the probability that both are white ?
A. 5/16
B. 2/13
C. 3/26
D. 5/39

Correct Op: D
n(S) = Number of ways of drawing 2 balls out of 13 = 13C2 = 13 x 12 / 2= 78 n(E) = No. of ways of drawing 2 balls out of 5 = 5C2 = 5 x 4 / 2 = 10 ∴ P(E) = n(E)/n(S) = 10/78 = 5/39

Question 7
Three unbiased coins are tossed. What is the probability of getting at most 2 heads ?
A. 1/4
B. 3/8
C. 7/8
D. 1/2

Correct Op: C
n(S) = (2)3 = 8 E = Event of getting 0, or 1 or 2 heads = {TTT, TTH, THT, HTT, HHT, HTH, THH} ⇒ n(E) = 7 ∴ P(E) = n(E)/n(S) = 7/8
 
Question 8
A brother and sister appear for an interview against two vacant posts in an office. The probability of the brother’s selection is 1/5th and that of the sister’s selections is 1/3rd. What is the probability that one of them is selected?
A. 1/5
B. 2/5
C. 1/3
D. 2/3

Correct Op: B
One of them can be selected in the following ways. Brother is selected and sister is not selected. or Brother is not selected and sister is selected. ∴ Required probability = 1/5 x 2/3 + 4/5 x 1/3 = 2/15 + 4/15 = 6/15 = 2/5
 
Question 9
Four whole number taken at random are multiplied together. The chance that the last digit of the product is 1, 3, 7, or 9 is ?
A. 16/625
B. 1/210
C. 8/125
D. 4/25

Correct Op: A
If the product of the four numbers ends in one of the digits 1, 3, 7 or 9, each number should have the last digit as one of these 4 digits. ∴ The number of favourable cases = 44 Total number of all possible cases = 104 Hence, the required probability =44/104 = 24/54 = 16/625
 
Question 10
The probability that a card is drawn from a pack of 52 cards will form a pack of 52 cards will be diamond or king being in?
A. 4/52
B. 4/13
C. 1/52
D. 2/13

Correct Op: B
Total ways = 52 There are 13 cards of diamond, 4 cards of king, but one card is king of diamond which is counted both in diamond and king cards ⇒ Favorable ways = 13 + 4 – 1 = 16 ∴ Required probability = 16/52 = 4/13