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Example: Suppose your football team has 10 returning athletes and 4 new members. How many ways can the coach choose one old player and one new one?
Solution: There are 10 ways to choose a returning player and 4 ways to choose a new one. Thus, there are 10 x 4 = 40 ways to choose one of each.
Example: Suppose we pick 2 numbers from 1, 2, 3, 4, 5 with replacement. Find the probability that one number is even.
Solution: Note that we want only one number to be even, not both, so we can rephrase this as: The first number is even AND the second number is odd OR the first number is odd AND the second number is even.
Use the addition and multiplication rules to calculate that there are (2 x 3) + (3 x 2) = 12 ways for this event to occur. Since there are 5 ways of choosing the first number AND 5 ways of choosing the second, S contains 5 x 5= 25 points.
The probability that one number is even is:
P(one number is even) = 12/25
Q. Converting Mixed Numbers to Improper Fractions? Ans. Converting a mixed number to an improper fraction is easy. A single multiplication, and then a single addition:
1+2+3+.....+n=1/2n(n+1)
Show that the points (3, 0), (4, 5), (-1, 4) and (-2, -1) taken in order are the vertices of a rhombus. Also find the area of the rhombus.
Illustration 1 In a described exam the scores for 10 students were given as: Student Mark (x) |x-x¯| A 60
show that one of the straight lines given by ax2+2hxy+by2=o bisect an angle between the co ordinate axes, if (a+b)2=4h2
(a) Determine the matrix that first rotates a two-dimensional vector 180° anticlockwise, and then per- forms a horizontal compression of the resulting vector by a factor 1/2 (leavi
Solve the subsequent proportion: Example: Solve the subsequent proportion for x. Solution: 5:x = 4:15 The product of the extremes is (5)(15) = 75. The produ
what is 10+5..
a man in rested rupee 800 is buying rupee 5 shares and then are selling at premium of rupee 1.15. He sells all the shares.find profit
Convert each of the following points into the specified coordinate system. (a) (-4, 2 Π /3) into Cartesian coordinates. (b) (-1,-1) into polar coordinates. Solution
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