Two coins are to be flipped. The first coin will land on heads with probability 0.6, the second with probability 0.7. Assume that the results of the flips are independent, and let X equal the total number of heads that result. (a) Find P{X=1}. (b) Determine E[X].

Step-by-step explanation:

P(X=1)  = P(first heads and second tails) +P(first tails and second heads)

            =P(first heads)×P(second tails)    +  P(first tails)  ×P(second heads)              

             because events are independent P(A∩B)  = P(A) ×P(B)

            = 0.6 ×0.3 + 0.4 ×0.7

            = 0.46

P(X=0)    = P(first tails and second tails)

               = 0.4  ×0.3

               =0.12

P(X=2)    =   P(first heads and second heads)

               = 0.6 ×0.7

               = 0.42

Mean   E(X)     =    0 ×0.12 + 1 × 0.46 + 2 ×0 0.42

                        =1.3            ( Because mean is ratio it can can be greater than 1 )

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.

there are 70 more legs than eyes at the dog show (196 – 126 = 70). dogs have two more legs than eyes, and humans have the same number of legs as eyes. thus 70 is twice the number of dogs at the show, so the number of dogs is half of 70, which is 35. to get the number of humans, subtract 35 from 63: 63 – 35 = 28.

step-by-step explanation: