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balandron [24]
2 years ago
13

Two chips are drawn at random and without replacement from a bag containing two blue chips and two red chips. Events A and B are

defined as follows. A: {At least one of the chips is blue}. B: {Both chips are red}. The events A and B are mutually exclusive.
Mathematics
1 answer:
BARSIC [14]2 years ago
5 0

Answer:

Yes, The events A and B are mutually exclusive event.

Step-by-step explanation:

Two chips are drawn at random and without replacement from a bag containing two blue chips and two red chips.

Total chips (n ) = 4

Two chips are chooses from 4 chips then the total possibilities are = \binom{4}{2}

total outcomes = \frac{4!}{(2!)(2!)} = 6

Let b_{1} and b_{2} denote blue chips and r_{1} and r_{2} denote red chips.

A: {At least one of the chips is blue} = { b_{1}b_{2 , b_{1}r_{1} , b_{1}r_{2} , b_{2}r_{1}, b_{2}r_{2} }

P( A) = \frac{5}{6}

B: {Both chips are red} = { r_{1}r_{2} }

P( B)  = \frac{1}{6}

(A\bigcup B)  = { b_{2}b_{1} , b_{1}r_{1} , b_{1}r_{2} , b_{2}r_{1} , b_{2}r_{2} ,r_{1}r_{2} }

P(A\bigcup B) = \frac{6}{6}

If A and B are mutuall exclusive

P(A\bigcup B) = P( A) + P( B)

P( A) + P( B)  = \frac{5}{6} + \frac{1}{6} = 1

P(A\bigcup B) = \frac{6}{6} = 1

Hence

P(A\bigcup B) = P( A) + P( B)

Then A and B are mutuall exclusive

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