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frutty
8 days ago
15

Two coins are to be flipped. The first coin will land on heads with probability 0.6, the second with probability 0.7. Assume tha

t 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].
Mathematics
1 answer:
PIT_PIT [3.9K]8 days ago
3 0

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)              

               since 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            ( Since mean is a ratio, it may exceed 1 )

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