Let's say a keep tossing a fair coin, until he get 2 consecutive heads, define x to be the number of tosses for this process; b keep tossing another fair coin, until he get 3 consecutive heads, define y to be the number of the tosses for this process. 1) calculate p{x> y}

A=Tossing a  fair coin, until getting  2 consecutive heads,

Minimum Number of tosses

 =(SF)(FS)(FF)(SS)

X =8 tosses

S=Success

F=Failure

B=Tossing a  fair coin, until getting 3 consecutive heads.

Minimum Number of tosses

 =(SFS)(FSS)(SSF)(SFF)(FSF)(FFS)(FFF)(SSS)

Y =24 Tosses

Probability of an event

table 3 represents a direct variation function. : )

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752