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

Question

3 months ago

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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].

1 answer:

PIT_PIT [12.4K] · Answer 1 · 2026-02-25T06:32:34+03:00

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 )