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A bag P contains 4 white balls and 3 black balls and a bag Q contains 5 white balls and 2 black balls. A ball is drawn at random from P and put into Q. Find the probability that the ball drawn from Q has: 1. The same color as that drawn from P; 2. A different color from that drawn from P;

Respuesta :

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Answer:

a)   [tex]P(S)=\frac{15}{28}[/tex]

b)   [tex]P(D)=\frac{13}{28}[/tex]

Step-by-step explanation:

From the question we are told that:

Bag A   [tex]W=4\\\\ Q=3[/tex]

Bag Q   [tex]W'=5\\\\ Q'=2[/tex]

Generally the equation for Probability of drawing W&B balls is mathematically given by

Bag A

[tex]P(W)=\frac{4}{7}P(Q)=\frac{3}{7}[/tex]

Since Ball is drawn and added to Bag Q

Bag Q

[tex]P(W)'=\frac{6}{8}\\\\ Q(B)'=\frac{2}{8}[/tex]

a)

Generally the equation for Probability of being the same is mathematically given by

[tex]P(S)=(P(W)*P(W'))+(P(B)*P(B)')[/tex]

[tex]P(S)=(\frac{4}{7}*\frac{6}{8})+(\frac{3}{7}*\frac{2}{8})[/tex]

[tex]P(S)=\frac{15}{28}[/tex]

b)

Generally the equation for Probability of NOT being the same is mathematically given by

[tex]P(D)=P(W)+P(B)'+(P(B)*P(W'))[/tex]

[tex]P(D)=(\frac{4}{7}*\frac{2}{8})+(\frac{3}{7}*\frac{6}{8})[/tex]

[tex]P(D)=\frac{13}{28}[/tex]

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