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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.
| Then, E | = {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)} |
| 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: | |||||||||||||||||
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.
|
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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: | ||||||||||||||||||||||||||||||||
Answer: Option C Explanation:
Let S be the sample space.
Let E = event of getting all the 3 red balls.
|
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