I neddd help with these questions all of them;

1. UseaVenndiagramtoverifythat AMBUC} ={AnB)u{AnG). 2. Two dice, identical except that one is green and the other is red, are tossed and the number of dots on the top face of each is observai. (a) \"'hat is the sample space for this experiment? b Would our sample space be different if both dice had the same color and therefore 3' you could not distinguish them? Explain your answer. (c) \"'hat would be the sample space if instead of observing the dots on the top of each die, you would just count the total number of dots at both dice? 3. A coin is ipped three times, and heads or tails is observed after each Hip. \"that is the sample space?I Indicate the outcomes in the event \"at least 2 heads are observed." 4. A coin is ipped, and it is noted whether hands or tails show. A die is tossed, and the number on the top face is noted. What is the sample space of this experiment? 5. A survey indicates rst whether a person is in the lower income group {L}, middle income group (M), or upper income group (U), and second which of these groups the father of the person is in. (a) Determine the sample space using the letters L, M, and U. (In) Find the outcomes in the set corresponding to the event E \"the person is in the lower income group." (c) Find the outcomes in the set corresponding to the event F \"the person is in the higher income group." (d) Find the sets: i. E U F ii. E n F iv. E c F0 v. EC U F0 (e) Find all pairs of sets listed in part (5d) that are mutuallyr exclusive. 5. lithe sample space S is dened as S = {11, 6,13}, with the probability of a, h and c denoted as 13(0), P(b) and P[c), respectively. If P(n) = P(b] = 2P(c], what is the value of Phil)? 7. A company has bids on two contracts. The},r believe that the probability of obtaining the rst contract is 0.4 and of obtaining the second contract is 0.3, while the probability of obtaining both contracts is 0.1. 8. Find the probability that they will obtain exactly one of the contracts. 9. Find the probability that they will obtain neither of the contracts