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GATE CSE 1996 | Question: 1.5

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Two dice are thrown simultaneously. The probability that at least one of them will have $6$ facing up is

  1. $\frac{1}{36}$

  2. $\frac{1}{3}$

  3. $\frac{25}{36}$

  4. $\frac{11}{36}$

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3 Answers

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Answer is (D)

$1- ($no. $6$ in both the dice $)=1-\left(\dfrac{5}{6} \times\dfrac{5}{6}\right)=\dfrac{11}{36}.$

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This question can be done simply as question is asking for at least one of them facing 6 ..

 

P(at least one 6 face up)= 1 - (none of them facing 6)

1 - ( 5/6 * 5/6)

1- 25/36

11/36..
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P(atleast one of dice will have 6 facing)  = 1 - P(none of dice have 6 facing up)

                                                                = 1 - ( 5/6 * 5/6)

                                                                 =1- 25/36

                                                                  = 11/36
 

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