Which of the following random variables is geometric?

a. the number of 5s when rolling a die 35 times
b. the number of spades dealt from a shuffled deck of 52 cards in a seven card hand
c. the number of heads when a coin is tossed 10 times
d. the number of digits in a randomly selected row until a 9 is found
e. the number of 8s in a row of 20 random digits

Solution given:

7.<OYM=15°base angle of isosceles triangle

<OYL=50°base angle of isosceles triangle.

<OYL=<OYM+<MYL

50°=15°+<MYL

<MYL=50°-15°

<MYL=35°

again;

<MOL=35*2=70°central angle is double of a inscribed angle.

18.

Solution given:

<PQR+<PSR=180°sum of opposite angle of a cyclic quadrilateral is supplementary

<PQS+42°+78°=180°

<PQS=180°-120°=60°

<PQS=60°

<SPR=42°inscribed angle on a same arc is equal

:.<QPS=18°+42°=60°

<QSR=18°inscribed angle on a same arc is equal

again.

<PSR=78°

<QSR+<PSQ=78°

18°+<PSQ=78°

<PSQ=78°-18°

<PSQ=60°

In ∆ PQS

<PSQ=60°

<QPS=60°

<PQS=60°

In triangle ∆PQS all the angles are equal.