Answer Show Hint: Calculate the number of possible outcomes for throwing two dice. Calculate the number of favourable outcomes for each of the cases. Use the fact that the probability of any event is the ratio of the number of favourable outcomes and the number of possible outcomes to calculate the probability of each of the events. Complete step-by-step solution - We have to calculate the probability of each of the events when two dice are thrown.We know that the total number of possible outcomes when two dice are thrown is $=6\times 6=36$.We know that the probability of any event is the ratio of the number of favourable outcomes and the number of possible outcomes.We will now calculate the probability of events in each case.(a) We have to calculate the probability that the sum of digits is a prime number.We will draw a table showing the sum of digits on rolling both the dice.
Probability means Possibility. It states how likely an event is about to happen. The probability of an event can exist only between 0 and 1 where 0 indicates that event is not going to happen i.e. Impossibility and 1 indicates that it is going to happen for sure i.e. Certainty. The higher or lesser the probability of an event, the more likely it is that the event will occur or not respectively. For example – An unbiased coin is tossed once. So the total number of outcomes can be 2 only i.e. either “heads” or “tails”. The probability of both outcomes is equal i.e. 50% or 1/2. So, the probability of an event is Favorable outcomes/Total number of outcomes. It is denoted with the parenthesis i.e. P(Event).
What is Sample Space? All the possible outcomes of an event are called Sample spaces. Examples-
Types of EventsIndependent Events: If two events (A and B) are independent then their probability will be
Mutually exclusive events:
Not Mutually exclusive events: If the events are not mutually exclusive then
What is Conditional Probability? For the probability of some event A, the occurrence of some other event B is given. It is written as P (A ∣ B)
Example- In a bag of 3 black balls and 2 yellow balls (5 balls in total), the probability of taking a black ball is 3/5, and to take a second ball, the probability of it being either a black ball or a yellow ball depends on the previously taken out ball. Since, if a black ball was taken, then the probability of picking a black ball again would be 1/4, since only 2 black and 2 yellow balls would have been remaining, if a yellow ball was taken previously, the probability of taking a black ball will be 3/4. What is the probability of getting twin prime numbers when two dice are thrown at a time?Solution:
Similar QuestionsQuestion 1: What is the probability of getting even numbers on both dice? Solution:
Question 2: What is the probability of getting pair with both odd numbers on two dices? Solution:
Question 3: What is the probability of getting a pair with one even and one odd number on two dices? Solution:
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