Question

If p is chosen at random from the set {1,2,3,4} and q is to be chosen at random from the set {1,4,9,16}, what is the probability that pq will be less than 16?​

Answer 1

Answer:

The sample space having 16 elements as shown in the attachment

So, elements less than 16 = 1,2,3,4,4,8,9,12

Number of favourable outcomes = 8

So, required probability is 8/16 = 1/2.

Answer 2

Answer:

The answer to the given question is 1/2

Step-by-step explanation:

The given data is

set p = {1,2,3,4}

set q = {1,4,9,16}

p is selected from set 1 and q is from set 2.

To find :

The probability that pq will be less than 16.

solution :

The set p and q will be expressed in the form of multiplication as

$\: \: 1 \: 2 \: 3 \: 4 \\ 1 \: 1 \: 2 \: 3 \: 4 \\4 \: 4 \: 8 \: 12 \: 16 \\ 9 \: 9 \: 18 \: 27 \: 36 \\ 16 \: 16 \: 32 \: 48 \: 64$

The sample space is n(s) = 16.

The sets which have a product less than 16 is

(1,1),(1,4),(1,3),(1,9),(2,1)(2,4)(3,3)(4,3)

let a be the event that pq will be less than 16.

The number of sets whose product is less than 16 is n(a)=8

The probability that pq will be less than 16 is n(a)/n(s)

substitute the values

$\frac{8}{16}$

The final answer to the given question is that the probability of pq will be less than 16 is 1/2

Hence the probability of the product being less than 16 is found.

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