Ram shoots every third penalty to goal.If he gets chance to shoot all 5 penalty shots.What is the probability that he converts (does) exactly 3 goals. > Ram shoots every third penalty to goal.If he gets chance to shoot all 5 penalty shots.What is the probability that he converts (does) exactly 3 goals. My Approach: p(Ram for every 3rd goal)=1/3 p(Not scoring goal)=2/3 p(he gets exactly 3 goals)=(1/3)^3*(2/3)^2 Is this Right?

What you have calculated is the probability Ram scores the first three shots and misses the last two shots, or that the result is $SSSMM$.

There are other ways to score exactly three shots. How many? They are the sequences of $3$ S and $2$ $M$. They are $\binom{2+3}{2}=\frac{5!}{2!3!}=10$.

They are the following:

$SSSMM$

$SSMSM$

$SMSSM$

$MSSSM$

$SSMMS$

$SMSMS$

$MSSMS$

$SMMSS$

$MSMSS$

$MMSSS$

Since each has probability $\frac{1}{3}^3\frac{2}{3}^2=\frac{4}{243}$ and they are all mutually exclusive we find that the probability of scoring exactly $3$ scores is $10\cdot\frac{4}{243}\approx 0.1646$