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X                                               Y Y=0 Y=1 Y=2X=0      0.32 0.03 0.01X=1 0.06 0.24 0.02X=2 0.02 0.03 0.27Find  P(X≤1, Y=1)

Question

Find P(X≤1, Y=1)

X 			 Y	Y=0	Y=1	Y=2
X=0	 	 	 0.32	0.03	0.01
X=1	 	 	 0.06	0.24	0.02
X=2	 	 	 0.02	0.03	0.27
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Solution

To find the probability P(X≤1, Y=1), we need to sum up the probabilities where X is less than or equal to 1 and Y is equal to 1.

From the table, we can see that the events where X≤1 and Y=1 are (X=0, Y=1) and (X=1, Y=1).

The probability of (X=0, Y=1) is 0.03 and the probability of (X=1, Y=1) is 0.24.

So, P(X≤1, Y=1) = P(X=0, Y=1) + P(X=1, Y=1) = 0.03 + 0.24 = 0.27.

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