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--------------------------------------------------------------------- A card is drawn from a deck of 52cards. Find the probability of getting a king or a heart or a red card. letA, B, C be the events of getting a king, a heart, a red card respectively. denoting union with u and intersection with n P(A) = 4 /52 [four kings] P(B)=13/52 [thirteen hearts] P(C)=26/52[twenty six red cards] P(A n B)=1/52 [the king of hearts] P(B n C)=13/52 [the thirteen hearts are all red] P(C n A)=2/52 [2 kings among the red cards] P(A n B n C )=1/52 [only the king of hearts is common to all three events] P[king OR heart OR redcard] =P[ A u B u C ] =
P(A)+P(B)+P(C)-P(AnB)-P(BnC)-P(CnA)+P(AnBnC)=4/52 +13/52 +26/52 -1/52 -13/52 -2/52 +1/52 =28/52=7/13 -------------- problem 2 Verify the
property that diagonals of a rhombus bisect each other at right angles for the rhombus with verticesA(0,5),B(-2,-2) C(5,0),D(7,7) diagonals are AC and BD using midpoint formula({x1+x2}/2 , {y1+y2}/2) midpoint of AC=({0+5}/2 , {5+0}/2)=(5/2 ,5/2) midpoint of BD=({-2+7}/2, {-2+7}/2)=(5/2,5/2) therefore midpoint of AC = midpoint of BD The diagonals bisect each other. using slope formula slope of AC=[{y2-y1}/{x2-x1}]=[(0-5)/(5-0)]=(-1) slope of BD=[(7-(-2))/(7-(-2))]=1 product of the slopes of AC and BD =(-1)*1 = (-1) AC and BD are at right angles to each other Hence verified
other questions and problems: * integral
calculus integration formula---------------------------------------------------------------------------------------------- trigonometric
identity and ratio of certain standard angles* list
of differentiation formula
*integral
calculus integration formula--------------------------------------------------------------------------------------- |
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