Are thrown simultaneously What is the probability of getting two numbers whose product is even?

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National University of Singapore

Given:

Two dice are thrown simultaneously

Concept used:

A dice has numbers from 1 to 6 i.e. {1, 2, 3, 4, 5, 6}.

Formula used:

Probability = (Total number of favourable outcome)/(Total number of outcome)

Calculation:

When two dice are thrown.

Then, The number of total possible outcome = 6 × 6 = 36

(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)

(2, 1), (2, 2),..............................., (2, 6)

............................................................

............................................................

(6, 1), (6, 2), ................................(6, 6)

To get the two numbers whose product is odd, both should be odd numbers.

So favourable outcome are:

(1,1), (1,3), (1,5), (3,1), (3,3), (3,5), (5,1), (5,3), (5,5)

Total number of favourable outcome = 9

Probability = (Total number of favourable outcome)/(Total number of outcome)

⇒ Probability = 9/36 = 1/4

∴ The probability of getting two numbers whose product is odd is 1/4.

Select the correct option from the given alternatives :

Two dice are thrown simultaneously. Then the probability of getting two numbers whose product is even is

`3/4`

Explanation;

Two dice are thrown.

∴ n(S) = 36.

Getting two numbers whose product is even, i.e., one of the two numbers must be even.

Let event A: Getting even number on first dice.

event B: Getting even number on second dice.

∴ n(A) = 18, n(B) = 18, n(A  ∩ B) = 9

∴ Required probability = P(A ∩ B)

= `("n"("A") + "n"("B") - "n"("A" ∩ "B"))/("n"("S"))`

= `(18 + 18 - 9)/36`

= `27/36`

= `3/4`

Concept: Concept of Probability

  Is there an error in this question or solution?

In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36.

P(E) =	n(E)	=	27	=	3	.
n(S)	36	4

Page 2

Exercise :: Probability - General Questions

• Probability - Important Formulas
• Probability - General Questions

11.	A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is:
A. B. C. D. Answer: Option C Explanation: Here, n(S) = 52. Let E = event of getting a queen of club or a king of heart. Then, n(E) = 2. P(E) = n(E) = 2 = 1 . n(S) 52 26

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12.	A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:
A. B. C. D. Answer: Option C Explanation: Let S be the sample space. Then, n(S) = number of ways of drawing 3 balls out of 15 = 15C3 = (15 x 14 x 13) (3 x 2 x 1) = 455. Let E = event of getting all the 3 red balls. n(E) = 5C3 = 5C2 = (5 x 4) = 10. (2 x 1) P(E) = n(E) = 10 = 2 . n(S) 455 91

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