Probability and Statistics - Essay Example

In calculating this one, you will consider the P(X=10) then subtract from the total probability value which is always equal to 1 (Schervish, 2011) and this is as shown below:P(X>10) = 1 – P(X=10)Note that the probability of P(X=10) is totally equal to the P(X=8). Hence this results toP(X>10) = 1- P(X=8)= 1 – 0.08= 0.922. If 53% of the members of the congress house are republicans, this then directly implies that the remaining 47% are democrats. This being the case, these figures can be expressed as decimals or rather probabilities as:Republicans 53/100 = 0.

53Democrats 47/100 = 0.47When 3 members are then chosen then in random the probability that they are democrats is calculated as follows:The first time picking the name the probability is of picking a democrat is o.47 or 47/100.The second time of picking, the total number of names has now reduced to the 99 hence; the probability of picking a democrat member is 46/99.The total number is furthermore reduced because the withdrawals are done without replacement (Schervish, 2011) and now the total remaining names are 98 thus the probability of getting a democrat a third time will be 45/98.

The probability of getting three democrats in the first 3 withdraws of names will eventually be = (47/100) X (46/99) X (45/98) = 97290/970200= 0.1002783 3. 64% being males, this implies that 36% are females. The assumption taken here is that the 54% tenured refers to the entire population and 46% are the untenured members of the university faculty. Gender and tenure being totally independent, thena) The probability of a male being picked is 64/100 and furthermore for the untenured cases, the probability reads at 46/100.

This implies that to get untenured male being picked from the population, then the product of the two scenarios is taken i.e. = (64/100) X (46/100)= 0.2944 or 2944/10,000 b) To get a tenured female, the evaluations will be as follows;Probability of females = 36/100Probability of tenure ship = 54/100Thus tenured female probability will be = (36/100) X (54/100)= 1944/10,000 or 0.19444. a) The republicans = 40The democrats = 35The probability of picking a democrat from this room will be evaluated and given as follows:Total number of members in the house = 40 + 35 = 75Total number of democrats = 35Hence probability (Schervish, 2011) of picking a democrat = (total number of democrats)/(total number of members in the house)= 35/75 = 0.4666667c) Out of the 75 members present in this house, only 6% are opposing.

This implies that 6% of 75 = 4.5 are opposing. This translates to (2/4.5) X (6/100) = 0.26667