Example:
The diagram shows two spinners, each of which is divided into 4 equal sectors. Each spinner has a pointer which, when spun, is equally likely to come to rest in any of the four equal sectors.
In a game, each pointer is spun once.
Find the probability that
a) the pointers will stop at the same number
b) the first spinner shows the larger number.
Solution:
Construct the probability diagram. Each dot represents a possible outcome according to the coordinates.
a) Let A = event of getting the same number on the two spinners.
From the probability diagram, n(A) = 4, n(S) = 16
P(A) =
b) Let B = event the first spinner shows the bigger number.
From the probability diagram, n(B) = 6
P(B) =Example:
Two fair dice are thrown together. Find the probability that the sum of the resulting number is
a) odd
b) a prime number
Solution:
Construct the following probability diagram showing the sums:Example:
X = {1, 2, 3} and Y = {4, 5, 6}. An element x is selected from X and an element y is selected from Y.
Complete the following probability diagrams for x + y and x × y
a) Find the probability that the sum x + y is:Solution:
a) The following probability diagrams for x + y and x × yb) The probability that the product xy is:
i) odd
Let S be the sample space, and C be the event that the product is odd.
From the probability diagram, n(C) = 2 ; n(S) = 9
P(C) =
ii) at most 10
Let S be the sample space, and D be the event that the product is at most 10.
From the probability diagram, n(D) = 5 ; n(S) = 9
P(D) =
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