ce- Name: Math 11-MACO Suppose that 18 cards are placed in a hat. The pictures o

Question

ce- Name: Math 11-MACO Suppose that 18 cards are placed in a hat. The pictures on the cards are shown above. One card is to be chosen at random. Let event. B-the symbol is black S the symbol is a square W the symbol is white C the symbol is a circle T the symbol is a triangle Find the following probabilities giving answers as reduced fractions: RBC) P( S and W) P(S or W) Are the events W and T independent? Explain. Are the events B and C independent? Explain. Are the events B and S mutually exclusive, independent, or neither? Explain.

Explanation / Answer

P(B)=12/18 =2/3 (as there are 12 black symbol out of 18)

P(C)=6/18=1/3

P(B|C)=P(B n C)/P(C)=4/6=2/3

P(C|B)=P(C n B)/P(B) =4/12=1/3

P(B|T)=7/7=1

P(T|B)=7/12

P(S|W)=4/6 =2/3

P(S and W)=4/18=2/9

P(S or W) =P(S)+P(W)-P(S and W) =(5/18)+(6/18)-(4/18)=7/18

are the events W and T are independent ? -No

as P(W n T)=0 which is not equal to P(W)*P(T)=(6/18)*(7/18) ; therefore not independent.

are the events B and C are  independent ? -Yes ; as P(B|C) is equal to P(B)

are the events B and S are mutuallly exclusive, independent or neither? -neither

as P(B n S)=1/18 which is not equal to 0 therefore not mutually exclusive

also P(B)*P(S)=(12/18)*(5/18) which is not equal to  P(B n S) therefore not  independent

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