Question

two dice are rolled until a sum of either 5 or 7 occurs. estimate the probability that a 5 occurs first g

Answer 1

Answer:

The correct answer is "$\frac{2}{5}$". A further solution is provided below.

Step-by-step explanation:

According to the question,

The probability of getting a 5 will be:

= $\frac{4}{36}$

= $\frac{1}{9}$

The probability of getting a 7 will be:

= $\frac{6}{36}$

= $\frac{1}{6}$

The probability of not a 5 nor a 7 will be:

= $1-[\frac{4}{36} +\frac{4}{36} ]$

= $\frac{26}{36}$

= $\frac{13}{18}$

Now,

For roll of 2 dice,

⇒ $P=\frac{1}{9} +{\frac{1}{9}\times (\frac{13}{18} ) }+{(\frac{1}{9} )\times (\frac{13}{18} )^2}+{\frac{1}{9}\times (\frac{13}{18} )^3 }+...$

        $=\frac{1}{9} [1+\frac{13}{18} +\frac{13^2}{18^2} +\frac{13^3}{18^3} +...]$

        $=\frac{1}{9} [\frac{1}{1-\frac{13}{18} } ]$

        $=\frac{1}{9} [{\frac{1}{\frac{5}{8} } ]$

        $=\frac{2}{5}$