Explanation: Probability of any sure event is always equal to 1 as the total number of favourable outcomes is equal to the total number of possible outcomes. **The probability of an impossible event is 0** because it cannot occur in any situation.

We know, probability of an event is either greater than or equal to 0 and always less than or equal to 1. Hence the probability of an event can never be negative. cannot be the probability of an event. Hence (A), (C), (D) **all lie between 0 and 1**.

A pair of dice is rolled. **The events of rolling a 5 and rolling a double have NO outcomes in common so the two events are mutually exclusive**. A pair of dice is rolled. The events of rolling a 4 and rolling a double have the outcome (2,2) in common so the two events are not mutually exclusive.

If an event cannot occur, then its probability is 0. The probability of an event which is very unlikely to happen is **closest to zero**.

Following are such examples ----

(ii) 'Sum-13' in case of throwing a pair of dice. In other words, An event E is called an impossible event **if P(E) = 0**. This happens when no outcome of the experiment is a favourable outcome.

What is the probability of a sure event? Explanation: Sure event has all outcomes in favour i.e. number of outcomes in favour equal to the total number of possible outcomes. And probability is **ratio of number of outcomes in favour to the total number of possible outcomes**. So, probability of sure event will be 1.

In mathematics, a proof of impossibility, also known as negative proof, proof of an impossibility theorem, or negative result is **a proof demonstrating that a particular problem cannot be solved as described in the claim, or that a particular set of problems cannot be solved in general**.

always 0

A statistical impossibility is **a probability that is so low as to not be worthy of mentioning**. Sometimes it is quoted as 10−50 although the cutoff is inherently arbitrary. Although not truly impossible the probability is low enough so as to not bear mention in a rational, reasonable argument.

**An event which is impossible to occur**, is called an impossible event. The probability of impossible event is always zero.

**-1.5** cannot exist as a probability value as it is greater than 1 and the value is negative, while probability, the possibility of happening an event, has the maximum value of 1, and it is always a positive number.

Probability (of an event) In an experiment, the probability of an event is **the likelihood of that event occuring**. Probability is a value between (and including) zero and one. If P(E) represents the probability of an event E, then: P(E) = 0 if and only if E is an impossible event.

If events A and B are mutually exclusive, then the probability of A or B is simply: **p(A or B)** **= p(A) + p(B)**.

The probability of an event is **a number describing the chance that the event will happen**. An event that is certain to happen has a probability of 1. An eventthat cannot possibly happen has aprobability of zero. If there is a chance that an event will happen, then itsprobability is between zero and 1.

Mutually exclusive events are events that can not happen at the same time. Examples include: **right and left hand turns, even and odd numbers on a die, winning and losing a game, or running and walking**.

The probability of an impossible event is **0**.

The probability of an impossible event is **0**. The probability of an event that is certain to occur is 1. For any event A, the probability of A is between 0 and 1 inclusive.

In statistics, the probability of an impossible event is equal to 0. For an impossible event, E = 0 and thus, P(E) = 0. For example, **the probability of drawing a green ball, out of a set of red balls is zero as getting a green ball when you just have red balls in the set**, is an impossible event.

What is the Probability of an Impossible Event and a Sure Event? **The probability of a sure event is always 1 while the probability of an impossible event is always 0**.

In probability, a set of events is collectively exhaustive **if they cover all of the probability space**: i.e., the probability of any one of them happening is 100%. If a set of statements is collectively exhaustive we know at least one of them is true.

1 remaining day can be Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday. Total of 7 outcomes, the favourable outcome is 1. ∴ probability of getting 53 Sundays = **1 / 7**.

Dated : 20-May-2022

Category : Education