Problem 1 :
Two dice are rolled, find the probability that the sum is
i) equal to 1 ii) equal to 4 iii) less than 13
Solution :
Sample space :
{(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)}
n(S) = 36
Let "A" be the event of getting sum equal to 1.
A = 0
n(A) = 0
p(A) = n(A)/n(S) = 0/36
p(A) = 0
(ii) equal to 4
Let "B" be the event of getting the sum equal to 4.
B = {(1, 3) (2, 2) (3, 1)}
n(B) = 3
p(B) = n(B)/n(S)
P(B) = 3/36
P(B) = 1/12
(iii) less than 13
C = {(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)}
n(C) = 36
p(C) = n(C)/n(S)
= 36/36
p(C) = 1
Problem 2 :
A manufacturer tested 7000 LED lights at random and found that 25 of them were defective. If a LED light is selected at random, what is the probability that the selected LED light is a defective one.
Solution :
Total number of bulbs n(S) = 7000
Number of defective bulbs = 25
Let ""A be the event of getting defective bulb
n(A) = 25
p(A) = n(A)/n(S)
p(A) = 25/7000
p(A) = 1/280
Problem 3 :
In a football match, a goalkeeper of a team can stop the goal, 32 times out of 40 attempts tried by a team. Find the probability that the opponent team can convert the attempt into a goal.
Solution :
Total number of match n(S) = 40
Let "A" be the event of the opponent team can convert attempt into goal
n(A) = 40 - 32 = 8
p(A) = n(A)/n(S)
P(A) = 8/40
P(A) = 1/5
Problem 4 :
What is the probability that the spinner will not land on a multiple of 3?
Solution :
Sample space = {1, 2, 3, 4, 5, 6 , 8}
n(S) = 8
Let "A" be the event of that the spinner will not land in multiple of 3.
A = {1, 2, 4, 5, 7, 8}
n(A) = 6
P(A) = n(A) / n(S)
P(A) = 6/8
P(A) = 3/4
Problem 5 :
Frame two problems in calculating probability, based on the spinner shown here.
Solution :
(i) What is the probability that the spinner will land on a multiple of 2 ?
(ii) What is the probability that the spinner will land on a number greater than 3 ?
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