In the first urn of 8 black and 9 white balls, in the second-2 black and 2 whites. From one of the urns, the ball took out a ball. The likelihood that this ball is black.
In the first urn 8 + 9 = 17 balls.
In the second urn 2 + 2 = 4 balls.
Put forward hypothesis:
H1 – the ball was taken from the first urn;
H2 – the ball was taken out of the second urn;
P (H1) = 1/2;
P (H2) = 1/2;
Event in – got a black ball.
The conditional probabilities of this event b with hypotheses are equal to:
P (B | H1) = 8/17;
P (B | H2) = 2/4 = 1/2; ·
According to the full probability formula, we find the likelihood of an event in after experience:
P (b) = p (h1) · p (b | h1) + p (h2) · p (b | h2) = (1/2 · 8/17) + (1/2 · 1/2) = 4 / 17 + 1/4 = 16/68 + 17/68 = 33/68 = 0.485.
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