A doctor claims of 60% of the patients he examines are allergic to some type of weed. What is the probability that (i) exactly 3 of his next 4 patients are allergic to weeds? (ii) none of his next 4 patients is allergic to weeds?

A doctor is to visit a patient. From the past experience, it is known that the probabilities that he will come by train, bus , scooter or by other means of transportation are respectiely 3/10,1/5,1/10 or 2/5 . The probabilities that he will be late are 1/4,1/3 and 1/12 if he comes by train, bus and scooter respectively but if he comes by other means of transport, then he will not be late. If the arrives late, find the probability that he comes by train.

You note that your officer is happy with 60% of your calls, so, you assign a probability of his being happy on your visit of 0.6 . You have noticed also that if he is happy, he accedes to your request with a probability 0 . 4 , whereas if he is not happy he accedes to the request with a probability of 0.1 . You call one day and he accedes to your request . What is the probability that your office was happy ?

A shopkeeper sells three types of seeds A_1, A_2a n dA_3 They are sold as a mixture where the proportions are 4:4:2 respectively. The germination rate of three types of seeds are 45%, 60% and 35%. Calculate the probability (i)that it will germinate given that the seed is of type A_3 . (ii)of a randomly chosen seed to germinate. (iii)That it is of type A_2 given that a randomly chosen seed does not germinate.

Mr. Sharma has 60 shares of N.V. 100rs and sells them when they are a premium of 60% . He invests the proceeds in shares of nominal value 50rs , quoted at 4% discount, and paying 18% dividend annually. Calculate (i) the sale proceeds (ii) the number of shares he buys and (iii) his annual dividend from the shares

Answer question numbers 3(a) - 3(d) on the basis of your understanding of the following paragraph and the related studied concepts: Around the year 1800, only 30 elements were known. Dobereiner in 1817 and Newlands in 1866 tried to arrange the then known elements and framed laws which were rejected by the scientists. Even after the ejection of the proposed laws, many scientists continued to search for a pattern that correlated the properties of elements with their atomic masses. The main credit for classifying elements goes to Mendeleev for his most important contribution to the early development of a Periodic table of elements wherein he arranged the elements on the basis of their fundamental property, the atomic mass and also on the similarity of chemical properties. The formula of their hydrides and oxides were treated as basic criteria for the classification of the elements. However, Mendeleev's classification also had some limitations as it could not assign the position to isotopes. He also left some gaps in the periodic table. 3(a) state Mendeleev's Periodic Law. 3(b) Why did Mendeleev leave some gaps in the Periodic table? 3(c) if the letter 'R' was used to represent any of the elements in the group , then the hydride and oxide of carbon would respectively be represented as (i) RH_4 , RO (ii) RH_4 , RO_2 (iii) RH_2 , RO_2 (iv) RH_2 , RO 3(d) isotopes are (i) atoms of an element with similar chemical properties but different atomic masses. (ii) atoms of different elements with similar chemical properties but different atomic masses. (iii) atoms of an element with different chemical properties but same atomic masses. (iv) atoms of different elements with different chemical properties but same atomic masses.