PROBABILITY AND REASONING
Section “C”
a) What is the probability of any event that is sure to be occurring like Day of Judgment? Please provide answer supplemented with the reason for making the answer.
b) What is the probability of any event that cannot occur like preference of LU Brand by any Muslim?
c) What is the probability of having an odd number when a dice is rolled?
d) What is the probability of having a sum more than twelve when a pair of dice
rolled once?
e) What is the probability of having a sum of exactly eight when a pair of dice rolled
once?
f) What is the probability of having a sum of two or above when a pair of dice rolled
once?
g) What is the probability of having a sum of eleven or above when a pair of dice
rolled once?
h) What is the probability of having queen if we draw a card at random from the pack of standard 52 cards?
i) What is the probability of having a red color card if we draw a card at random from the pack of standard 52 cards?
j) What is the probability of having queen of spade if we draw a card at random from the pack of standard 52 cards?
k) What is the probability of having jack of club if we draw a card at random from the pack of standard 52 cards?
Answers
Answer:
isn't too long question ??????
Answer:
Some important points:
1) P(A) is always between 0 and 1
0 ≤ P ≤ 1
2) P(∅) = 0
3) P(S) = 1
a) What is the probability of any event that is sure to be occurring like Day of Judgment? Please provide answer supplemented with the reason for making the answer.
Ans: Probability of any event that is sure to be occurring is always equal to 1
P = 1
b) What is the probability of any event that cannot occur like preference of LU Brand by any Muslim?
Ans: Probability of any event that cannot occur is always 0.
P = 0
c) What is the probability of having an odd number when a dice is rolled?
S = {1, 2, 3, 4, 5, 6}
A = {1, 3, 5}
P(A) = 3/6 = 1/2 = 0.5
d) What is the probability of having a sum more than twelve when a pair of dice rolled once?
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)}
A = {∅}
P(A) = 0
e) What is the probability of having a sum of exactly eight when a pair of dice rolled once?
A = {(2,6) , (3,5) , (4,4) , (5,3) , (6,2)}
P(A) = 5/36
f) What is the probability of having a sum of two or above when a pair of dice rolled once?
Since, all the elements of set S are the elements of set A.
So, P(A) = 1
g) What is the probability of having a sum of eleven or above when a pair of dice rolled once?
A = {(5,6) , (6,5) , (6,6)}
P(A) = 3/36 = 1/12
h) What is the probability of having queen if we draw a card at random from the pack of standard 52 cards?
Black
13 - Spades (Ace, 2, 3,...., 10, J, Q, K)
13 - Clubs (Ace, 2, 3,...., 10, J, Q, K)
Red
13 - Hearts (Ace, 2, 3,...., 10, J, Q, K)
13 - Diamonds (Ace, 2, 3,...., 10, J, Q, K)
Total no. of cards = 52
No. of favorable outcomes = 4
P(A) = 4/52 = 1/13
i) What is the probability of having a red color card if we draw a card at random from the pack of standard 52 cards?
Total no. of cards = 52
No. of favorable outcomes = 13 + 13 = 26
P(A) = 26/52 = 1/2
j) What is the probability of having queen of spade if we draw a card at random from the pack of standard 52 cards?
Total no. of cards = 52
No. of favorable outcomes = 1
P(A) = 1/52
k) What is the probability of having jack of club if we draw a card at random from the pack of standard 52 cards?
Total no. of cards = 52
No. of favorable outcomes = 1
P(A) = 1/52