What you are doing wrong is assuming that each of those possible outcomes is equally likely. Tossing the two coins there are four possible outcomes: Head, Head; Head, Tail; Tail, Head; Tail, Tail, each with probability 1/4. In case of the outcome "Head, Head", two die are rolled. In this case, the outcomes and their probabilities are 2: prob 1/36; 3: prob 2/36= 1/18; 4: prob 3/36= 1/12; 5: prob 4/36= 1/9; 6: prob 5/36; 7: prob 6/36= 1/6; 8: prob 5/36; 9: prob 4/36= 1/9; 10: prob 3/36= 1/12; 11: prob 2/36= 1/18; 12: prob 1/36; The probability of "odd" is 1/18+ 1/9+ 1/6+ 1/9+ 1/18= 9/18= 1/2. Since the probability of this case is 1/4, multiply that by 1/4: 1.8. In the case of "Heads, Tails" or "Tails, Heads" we roll a single die so the probability of any one number is 1/6. There are 3 odd numbers so the probability of "odd" is 3/6= 1/2 also. The probability of this case is 1/2 so multiply by 1/2: 1/4. in the case of "Tails, Tails" we do not roll any die so the "sum" is 0. That is even so the probability of "odd" in this case is 0. The overall probability of "odd" is 1/8+ 1/4= 3/8.
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. Solution:
Similar QuestionsQuestion 1: What is the probability of getting a sum of 11 on both dice? Solution:
Question 2: What is the probability of getting the sum of 12? Solution:
Question 3: What is the probability of getting the sum of 9 with two dice? Solution:
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