If A is an event of getting 13 by throwing two unbiased six-faced dice, then A is called
More than one of the above
Understanding Two Dice Throws
When we throw two unbiased six-faced dice, each die can land on any number from 1 to 6. The result of throwing two dice is the sum of the numbers shown on the top faces of both dice.
To find the possible sums, we can consider the minimum and maximum values:
- Minimum sum: When both dice show 1, the sum is $1 + 1 = 2$.
- Maximum sum: When both dice show 6, the sum is $6 + 6 = 12$.
All possible sums range from 2 to 12. Let's look at the possible outcomes for each die and their sums:
| Die 1 \ Die 2 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| 6 | 7 | 8 | 9 | 10 | 11 | 12 |
As shown in the table, the highest possible sum when throwing two standard six-faced dice is 12.
Analyzing Event A: Getting a Sum of 13
The event A is defined as getting a sum of 13 by throwing two unbiased six-faced dice. Based on our analysis of possible sums (which range from 2 to 12), a sum of 13 cannot be achieved.
What is an Impossible Event?
In probability, an impossible event is an event that cannot occur. The probability of an impossible event is always 0.
What is a Null Event?
In set theory applied to probability, the sample space is the set of all possible outcomes. An event is a subset of the sample space. A null event (or empty event) is an event that corresponds to the empty set ($\emptyset$) in the sample space. It represents an outcome or set of outcomes that is not possible within the given sample space.
Connecting Event A to Definitions
Since it is impossible to get a sum of 13 when throwing two standard six-faced dice, the event A cannot occur. This perfectly matches the definition of an impossible event.
Furthermore, the set of outcomes for event A is empty because there are no outcomes in the sample space (all pairs of numbers from 1 to 6) that sum up to 13. An event corresponding to the empty set is by definition a null event.
Therefore, the event A is both an impossible event and a null event.
Considering the given options:
- Option 1: a certain event (An event that is sure to happen, probability 1). Event A is not a certain event.
- Option 2: a null event. Event A is a null event.
- Option 3: an impossible event. Event A is an impossible event.
- Option 4: More than one of the above. Since Event A is both a null event and an impossible event, this option is correct.
Both option 2 and option 3 correctly describe event A. Thus, the event A is called both a null event and an impossible event.
Important Questions from Probability of Random Experiments
A six faced die is a biased one. It is thrice more likely to show an odd number than to show an even number. It is thrown twice. The probability that the sum of the numbers in the two throws is even is
A coin is biased so that a head is twice as likely to occur as a tail, if the coin is tossed three times, what is the probability of getting exactly two tails?
From two well shuffled pack of cards what is the probability of getting one Jack from the first one and a King from the second?
One summer, Peter visits 4 villages (A, B, C and D) in a random order. Find the probability that he visits (i) A before B (ii) A before B and B before C respectively?
An international team has two boxers picked for an international sport event. What is the probability that both the boxers are men given that at least one of them is a man?
