Q24 of 26 Page 1

A Bag I contains 5 red and 4 white balls and a Bag II contains 3 red and 3 white balls. Two balls are transferred from the Bag I to the Bag II and then one ball is drawn from the Bag II. If the ball drawn from the Bag II is red, then find the probability that one red ball and one white ball are transferred from the Bag I to the Bag II.

OR


Find the mean, the variance and the standard deviation of the number of doublets in three throws of a pair of dice.

Given Data:


• Bag I contains 5 red and 4 white balls


• Bag II contains 3 red and 3 white balls


Calculation:


Two balls are transferred from the Bag I to the Bag II


Three possibilities:


• Ball transferred is white, E1




• Ball transferred is red, E2




• One ball is red and other is white, E3




• The ball drawn from the Bag II is red, A


Since this happens after one of the events E1, E2, E3 already happened.


Now bag II has 6 balls,





Probability that one red ball and one white ball are transferred from the Bag I to the Bag II is given by Baye’s Theorem





OR


Given data:


Two dice thrown thrice


Calculation:


Total outcomes are 6x6 =36


Favorable outcomes are (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6),




There can be these situations


• No doublets


• Exactly 1 time doublets appear


• Exactly 2 times doublets appear


• 3 time doublets appear


Let X be random variable representing these situations


Now X = 0, 1, 2, 3












More from this chapter

All 26 →
22

Using integration, find the area bounded by the tangent to the curve 4y = x2 at the point (2, 1) and the lines whose equations are x =2y and x = 3y–3.

 23

Find the distance of the point from the plane 3 x + y – z + 2 = 0 measured parallel to the line . Also, find the foot of the perpendicular from the given point upon the given plane.

OR


Find the equation of the plane passing through the line of intersection of the planes and and passing through the point (3, –2, –1). Also, find the angle between the two given planes.

 25

A farmer wants to construct a circular garden and a square garden in his field. He wants to keep the sum of their perimeters 600 m. Prove that the sum their areas is the least, when the side of the square garden is double the radius of the circular garden. Do you think that a good planning can save energy, time and money?

 26

A manufacturing company makes two models A and B of a product. Each piece of model A requires 9 hours of labour for fabricating and 1 hour for finishing. Each piece of model B requires 12 hours of labour for fabricating and 3 hours for finishing. The maximum number of labour hours, available for fabricating and for finishing, are 180 and 30 respectively. The company makes a profit of Rs 8000 and Rs 12000 on each piece of model A and model B respectively. How many pieces of each model should be manufactured to get maximum profit? Also, find the maximum profit.