Q2: a) A group of friends decided to visit hill station (say H) in their vacations. To reach their destination they can follow two routes. The first directly connects H to K, whereas the second passes through G. Sometimes because of the weather conditions (snow falling), travelers cannot travel between B and A. If there is a forecast of snow for the next day, one can assume (on the basis of prior information) P(H) = 0.6, P(K) = 0.7, P(G) = 0.4, P(G|K) = 0.5 and P(H | GnK) = 0.4. Use the concepts of probability to find out the probability: i. That the traveler will be able to reach K from H? (2) ii. That the traveler will be able to drive from H to K by way of G? (2) iii. Which route should be taken in order to maximize his chance to reach K? (2) b) A box contains 4 pink balls 3 yellow marbles. A marbles is drawn. If the marbles is pink, it is kept out of the box and a second marbles is drawn from the box. If the marbles is yellow, then It is put back in the box and a pink marbles is added to the box. Then a second marbles is drawn from the box. Use the concepts of probability to find out the probability: i. that both marbles drawn are pink? (2.5) ii. If the second drawn marbles is pink, what is the probability that the first drawn marble was yellow? (2.5) Q2: a) A group of friends decided to visit hill station (say H) in their vacations. To reach their destination they can follow two routes. The first directly connects H to K, whereas the second passes through G. Sometimes because of the weather conditions (snow falling), travelers cannot travel between K and H. If there is a forecast of snow for the next day, one can assume (on the basis of prior information) P(H) = 0.6, P(K) = 0.7, P(G)= 0.4, P(G|K) = 0.5 and P(H| GnK) = 0.4. Use the concepts of probability to find out the probability: i, That the traveler will be able to reach K from H? traveler will be able to drive from H to K by way of G? ) ii. That the iii. Which route should be taken in order to maximize his chance to reach K? ( b) A box contains 4 pink balls 3 yellow marbles. A marbles is drawn. If the marbles is pink, it is kept out of the box and a second marbles is drawn from the box. If the marbles is yellow, then It is put back in the box and a pink marbles is added to the box. Then a second marbles is drawn from the box. Use the concepts of probability to find out the probability: i. that both marbles drawn are pink? ii. If the second drawn marbles is pink, what is the probability that the first drawn marble was yellow?