A six-sided dice is rolled and a four-sided dice is rolled and a coin is tossed.Considering this as a probability experiment, what is the size of the sample space?[Text Box]SubmitYou have used 0 of 1 attemptSave---An EventIn the context of the probability experiment just described (6-sided dice and 4-sided dice thrown and coin tossed): Consider the event in which the two face-up numbers on the two dice add to 8.What is the size of this set?[Text Box]SubmitYou have used 0 of 2 attemptsSave | Reset---Probability of an event (1/2)What is the probability of the event just described?Write your answer as a fraction of integers. For example, if the answer were 17/20 then enter 17/20 with no spaces or other symbols. You may reduce the fraction by cancelling factors common to the numerator and denominator but you do not need to do this.[Text Box]SubmitYou have used 0 of 1 attemptSave---Probability of an event (2/2)What is the probability that at least one 4 appears with the coin heads up?Write your answer as a fraction of integers. For example, if the answer were 17/20 then enter 17/20 with no spaces or other symbols. You may reduce the fraction by cancelling factors common to the numerator and denominator but you do not need to do this.[Text Box]Save

If the probability of getting selected for each outcome is equal then such outcomes can be termed as equally likely outcomes. For equally likely outcomes, the probability of favorable event can be given by dividing the number of favorable outcomes, with the total number of outcomes. Probability of favorable event=Number of favorable outcomesTotal number of outcomes For the experiment in which a six sided die is rolled, a four sided die is rolled and a coin is tossed, all the outcomes would be equally likely. Therefore, the above mentioned formula can be used to calculate the required probabilities.(a): Rolling of a six sided die has six outcomes, its sample space can be given as S1={1, 2, 3, 4, 5, 6}. Rolling of a four sided die has four outcomes, its sample space can be given as S2={1, 2, 3, 4}. Tossing of a coin has two outcomes, its sample space can be given as, S3={H, T}. For the experiment in which a six sided die is rolled, a four sided die is rolled and a coin is tossed, the sample space will have 6·4·2=48 outcomes. Therefore, the size of the sample space for this experiment is 48.(b): The outcomes of the experiment can be expressed as a,b,c, where a be the number which turns up for six sided die, b be the number which turns up for four sided die, and c be the outcome of coin. Assume E1 represents the event in which the two face-up numbers on the two dice add to 8. The favorable outcomes for this event to happen are {6,2,H, 5,3,H, 4,4,H, 6,2,T, 5,3,T, 4,4,T}. This suggests that the sample size for this set is 6. (c): The total number of outcomes for the experiment is 48 and all are equally likely to happen. For event E1: The number of favorable outcomes is 6. By using the formula Probability of favorable event=Number of favorable outcomesTotal number of outcomes , calculate the required probability PE1. PE1=Number of favorable outcomesTotal number of outcomes =648=18 Therefore, the probability that the two face-up numbers on the two dice add to 8, is 18.(d): Assume E2 represents the event in which at least one 4 appears with the coin heads up. The favorable outcomes for this event to happen are {6,4,H, 5,4,H, 4,4,H, 3,4,H, 2,4,H, 1,4,H, 4,1,H, 4,2,H, 4,3,H}. The total number of outcomes for the experiment is 48 and all are equally likely to happen. For event E2: The number of favorable outcomes is 9. By using the formula Probability of favorable event=Number of favorable outcomesTotal number of outcomes , calculate the required probability PE2. PE2=Number of favorable outcomesTotal number of outcomes =948=316 Therefore, the probability that at least one 4 appears with the coin heads up, is 316.