Given that
X = { x : x is an integer and 5 ≤ x ≤ 10 }
Y = { y : y is a multiple of 3 and 1 ≤ y ≤ 10 }
An element is chosen at random from each set.
Write down the total number of possible outcomes.
Using a probability diagram or otherwise, find the probability that:
(i) the product xy is a perfect square.
(ii) the product xy is an odd number.
(iii) the product xy > 20.
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Answer:
X = { x : 5, 6, 7, 8, 9, 10}
Y = { y : 3, 6, 9}
Total number of outcomes = 6 numbers * 3 numbers = 18
(i) Perfect squares = 6² and 9²
so, probability that product xy is a perfect square = 2/18 = 1/9
(ii) xy is an odd number means both x and y must be odd numbers
Number of odd numbers in x = 3
Number of odd numbers in y = 3
so, probability that product xy is an odd number = 3 * 3 / 18 = 1/2
(iii) Number of terms of xy < 20 : 5 * 3, 6 * 3
===> only 2 terms.
So, 16 terms are greater than 20
Probability of product xy > 20 = 16/18 = 8/9
