1. 10 people are lined up in a row in random order. what is the probability that 2 friends will stand side by side?

My try $$(9!*2!)/10!=0,2$$

1. The shooter is shooting in the moving target. The probability hitting it at the beginning of the shooting is 0.8, and after each shot is reduced by 0.1. Find the probability that the shooter will hit the third time.

My try

so, after 2nd shoot probability is 0,7, after 2rd - 0,6

$$P(notAnotBC)=P(notA)*P(notB)*P(C)=0,2*0,3*0,6$$

or is formula wrong?

• Both answers look good. As a side note, +1 to your answer, for showing good work. For me, the upvote pertains regardless of whether your work contains a mistake, which it doesn't. Commented Mar 29, 2021 at 11:38
• For the second question, it is not clear to me whether the target can be hit multiple times like an archery target, or if it can only be hit once like a clay pigeon. After the shooter successfully hits the target, do they necessarily stop shooting? If not, then you missed the possibilities of $ABC,AB^cC,$ and $A^cBC$, which you should recognize with the case you referred to all add up to $C$. Commented Mar 29, 2021 at 12:12