An unfair coin with Pr[H] = 0.6 is flipped. If the flip results in a head, a marble is selected at random from a urn containin g 4 red and 6 blue marbles. Otherwise, a marble is selected from a different urn containing three red and five blue marbles. If the selected marble selected is red, what is the probability that the flip resulted in a head?
1 answer:
Answer:
0.6154
Step-by-step explanation:
Using Baye's theorem, the probability that the flip resulted in a head If the selected marble selected is red is given by;
P( H | R ) = (P( R | H ) × P( H ))/[(P( R | H ) × P( H)) + (P( R | -H ) × P( -H ))]
We can deduce that;
P( R | H ) = 4/10 = 0.4
P( R | -H ) = 3/8 = 0.375
P( -H ) = 1 - P( H )
We are given P(H) = 0.6
Thus;
P( -H ) = 1 - P( H ) = 1 - 0.6 = 0.4
Plugging in the derived values into the derived Baye's theorem, we have;
P( H | R ) = [0.4 × 0.6] /[(0.4 × 0.6) + (0.375 × 0.4)]
P( H | R ) = 0.6154
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