Question

Two dice are thrown simultaneously. what is the probability of getting two numbers whose product is odd ?

Answer 1

Given : Two dice are thrown simultaneously.

To find : the probability of getting two numbers whose product is odd

Solution:

Each dice has numbers from 1 to 6

Two Dice are thrown

Possible outcomes=  6 *  6

= 36

getting two numbers whose product is odd

to get odd products both numbers should be odd

Probability of getting odd number in each dice

= 3/6  = 1/2

Probability of  getting two numbers whose product is odd

= (1/2)(1/2)

= 1/4

1/4 is the probability of getting two numbers whose product is odd

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Answer 2

Given:

Two dice are thrown simultaneously.

To Find:

What is the probability of getting two numbers whose product is odd ?

Solution:

Here two dice are thrown simultaneously, so outcome are:

Outcome of two dice = (x,y)

Where x belongs to outcome of first dice, so value of x are:

x = {1, 2, 3, 4, 5, 6}

Means total number of outcome of first dice = 6

Where y belongs to outcome of second dice, so value of y are:

y = {1, 2, 3, 4, 5, 6}

Means total number of outcome of second dice = 6

⇒Total number of outcome of two dice = 6×6 = 36       ...1)

Getting two numbers whose product is odd, it means:

x× y = Odd Number

This is only possible when:

x = {1 , 3, 5}

y = {1 , 3, 5}

So favourable outcome are:

Favourable outcome =(1,1) ,(1,3) , (1,5),(3,1) ,(3,3) , (3,5),(5,1) ,(5,3) , (5,5)

So total number of favourable outcome = 9      ...2)

We know formula of probability:

$\mathbf{Probability = \dfrac{Total\ number\ of\ favourable\ outcome}{Total\ number\ of\ outcome}}$

$\mathbf{Probability = \dfrac{9}{36}}$

$\mathbf{Probability = \dfrac{1}{4}}$

Probability = 0.25 = 25%