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CBSE Class 12-science Answered

1)    1)   Coloured balls are distributed in three bags as shown in the following table:

Bag

Black

White

Red

1

1

2

3

2

2

4

1

3

4

5

3

 

A bag is selected at random and then two balls are drawn randomly from the selected bag. They happen to be black and red. What is the probability that they come from bag 1 ?

2)    2)       A girl throws a die. If she gets 5 or 6, she tosses a coin three times and notes the  no. Of heads. If she gets 1,2,3 or 4 she tosses a coin once and notes whether head or tail is obtained. If she obtained exactly one head , what is the probability that she throws 1,2,3 or 4 with the die?

 

 

Asked by vandanashikha | 13 Feb, 2015, 10:44: PM
answered-by-expert Expert Answer
L e t space E subscript 1 comma space E subscript 2 comma space E subscript 3 comma space a n d space A space d e n o t e space t h e space f o l l o w i n g space e v e n t s colon E subscript 1 equals B a g space 1 space i s space c h o s e n E subscript 2 equals B a g space 2 space i s space c h o s e n E subscript 3 equals B a g space 3 space i s space c h o s e n A equals t w o space b a l l s space d r a w n space a t space r a n d o m space a r e space r e d space a n d space b l a c k. S i n c e space o n e space o f space t h e space b a g space i s space c h o s e n space a t space r a n d o m comma space P open parentheses E subscript 1 close parentheses equals 1 third semicolon P open parentheses E subscript 2 close parentheses equals 1 third semicolon P open parentheses E subscript 3 close parentheses equals 1 third semicolon A s s u m e space t h a t space b a g 1 space i s space c h o s e n. N o w space b a g space 1 space c o n t a i n s space 1 space b l a c k space b a l l comma space 2 space w h i t e space b a l l s space a n d space 3 space r e d space b a l l s. T h u s space t h e space p r o b a b i l i t y space o f space d r a w i n g space a space r e d space a n d space a space b l a c k space b a l l space i s space P open parentheses A divided by E subscript 1 close parentheses equals fraction numerator C presuperscript 3 subscript 1 cross times C presuperscript 1 subscript 1 over denominator C presuperscript 6 subscript 2 end fraction equals 3 over 15 equals 1 fifth A s s u m e space t h a t space b a g 2 space i s space c h o s e n. N o w space b a g space 2 space c o n t a i n s space 2 space b l a c k space b a l l s comma space 4 space w h i t e space b a l l s space a n d space 1 space r e d space b a l l. T h u s space t h e space p r o b a b i l i t y space o f space d r a w i n g space a space r e d space a n d space a space b l a c k space b a l l space i s space P open parentheses A divided by E subscript 2 close parentheses equals space fraction numerator C presuperscript 1 subscript 1 cross times C presuperscript 2 subscript 1 over denominator C presuperscript 7 subscript 2 end fraction equals 2 over 21 A s s u m e space t h a t space b a g 3 space i s space c h o s e n. N o w space b a g space 3 space c o n t a i n s space 4 space b l a c k space b a l l s comma space 5 space w h i t e space b a l l s space a n d space 3 space r e d space b a l l. T h u s space t h e space p r o b a b i l i t y space o f space d r a w i n g space a space r e d space a n d space a space b l a c k space b a l l space i s space P open parentheses A divided by E subscript 3 close parentheses equals space fraction numerator C presuperscript 4 subscript 1 cross times C presuperscript 3 subscript 1 over denominator C presuperscript 12 subscript 2 end fraction equals 2 over 11 W e space n e e d space t o space f i n d space P open parentheses E subscript 1 divided by A close parentheses. space B y space B a y e apostrophe s space T h e o r e m comma space w e space h a v e comma space P open parentheses E subscript 1 divided by A close parentheses equals fraction numerator P open parentheses E subscript 1 close parentheses cross times P open parentheses A divided by E subscript 1 close parentheses over denominator P open parentheses E subscript 1 close parentheses cross times P open parentheses A divided by E subscript 1 close parentheses plus P open parentheses E subscript 2 close parentheses cross times P open parentheses A divided by E subscript 2 close parentheses plus P open parentheses E subscript 3 close parentheses cross times P open parentheses A divided by E subscript 3 close parentheses end fraction rightwards double arrow space P open parentheses E subscript 1 divided by A close parentheses equals fraction numerator 1 third cross times 1 fifth over denominator 1 third cross times 1 fifth plus 1 third cross times 2 over 21 plus 1 third cross times 2 over 11 end fraction rightwards double arrow space P open parentheses E subscript 1 divided by A close parentheses equals fraction numerator 1 fifth over denominator 1 fifth plus 2 over 21 plus 2 over 11 end fraction rightwards double arrow space P open parentheses E subscript 1 divided by A close parentheses equals fraction numerator 1 fifth over denominator 551 over 1155 end fraction rightwards double arrow space P open parentheses E subscript 1 divided by A close parentheses equals 231 over 551
Answered by Vimala Ramamurthy | 14 Feb, 2015, 12:18: PM

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