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  • I need help with An unbiased coin is tossd. If the outcome is a head then a pair of unbaised dice is rolled and the sum of the numbers otained on them is noted. If the toss of the coin results in tails then a card from a well-suffled pack of nine cards nu

An unbiased coin is tossd. If the outcome is a head then a pair of unbaised dice is rolled and the sum of the numbers otained on them is noted. If the toss of the coin results in tails then a card from a well-suffled pack of nine cards numbered 1,2,3,.....,9 is randomly picked and the number on the card is noted. The probability that the noted number is either 7 or 8 is:

  • Option 1)

     

    13/36

  • Option 2)

     

    15/72

  • Option 3)

     

    19/72

  • Option 4)

     

    19/36

Answers (1)

best_answer

 

Probability of occurrence of an event -

Let S be the sample space then the probability of occurrence of an event E is denoted by P(E) and it is defined as 

P\left ( E \right )=\frac{n\left ( E \right )}{n\left ( S \right )}

P\left ( E \right )\leq 1

P(E)=\lim_{n\rightarrow\infty}\left(\frac{r}{n} \right )

 

 

- wherein

Where n repeated experiment and E occurs r times.

 

 

Independent events -

If A and B are independent events then probability of occurrence of A is not affected by occurrence or non occurrence of event B.

\therefore P\left ( \frac{A}{B} \right )= P\left ( A \right )

and    \dpi{100} \therefore P\left ( A\cap B \right )= P\left ( B \right )\cdot P\left ( \frac{A}{B} \right )

so  \therefore P\left ( A\cap B \right )= P\left ( A \right )\cdot P \left ( B \right )= P\left ( AB \right )

-

From the concept

getting head or tail, probability is \frac{1}{2}

Now,

Start \overset{\frac{1}{2}}{\rightarrow } H\rightarrow sum 7 or 8 \Rightarrow \frac{11}{36}

      \overset{\frac{1}{2}}{\rightarrow } T \rightarrow number 7 or 8\Rightarrow \frac{2}{9}

P(A) = \frac{1}{2} \times \frac{11}{36} + \frac{1}{2} \times \frac{2}{9}

= \frac{19}{72}


Option 1)

 

13/36

Option 2)

 

15/72

Option 3)

 

19/72

Option 4)

 

19/36

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