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Question: You roll a standard number cube. What is \(P\) (number greater than \(2\))?...

You roll a standard number cube. What is PP (number greater than 22)?

Explanation

Solution

Here we have to calculate the probability of getting a number greater than 22 when a dice is rolled. So, we have to form Probability of an event which can be defined as the ratio of a number of cases favourable to a particular event to the number of all possible cases. Probability can be calculated by the formula P(E)=Number of favourable outcomes to ENumber of all possible outcomes of experimentP(E) = \dfrac{\text{Number of favourable outcomes to E}}{\text{Number of all possible outcomes of experiment}}

Complete step by step answer:
We have to calculate the probability of getting a number greater than 22 when a dice is rolled. Probability can be simply defined as the possibility of something happening. It is the extent to which an event is likely to occur, measured by the ratio of the favourable cases to the whole number of cases possible. All the possible outcomes of a random experiment when put together is called a sample space.The probability of an event can be defined by the following formula
P(E)=Number of favourable outcomes to ENumber of all possible outcomes of experimentP(E) = \dfrac{\text{Number of favourable outcomes to E}}{\text{Number of all possible outcomes of experiment}}

According to the question one dice is rolled so total number of outcomes =6 = 6. To obtain a number greater than 22 we need that the dice should show 3,4,5,63,4,5,6.So favourable outcomes =4 = 4. Therefore, the probability of getting a number greater than 22 when a dice is rolled.Use the probability formula which is mentioned above. So,
⇒\Rightarrow P(E)=46P(E) = \dfrac{4}{6}
On further simplifying we get
∴P(E)=23\therefore P(E) = \dfrac{2}{3}

Hence, the probability of getting a number greater than 22 when a dice is rolled is 23\dfrac{2}{3}.

Note: The probability of an impossible event is 00 and the probability of a sure event is 11. The probability related to the same event will lie between 00 and 11. Hence the probability of an event is always greater or equal than zero but can never be less than zero. For mutually exclusive events, the probability of either of the events happening is the sum of the probability of both the events happening.