Year 8 maths homework help please!

[Lilamani]

DD is studying probability, which was never my strong point. Could anyone help with these questions please?

A number generator produces two digits. Each digit is generated randomly. It can be any digit from 0 to 9. Find the probability that there are no 0s.

Ahmad plays chess against his father. Ahmad's probability of winning is 0.1. His probability of losing is 0.3. Find the probability that his father will not win.

DD has completed the rest of the homework and asked if I could help with these two. The fact that she's learned in school is that if the probability of an outcome of an event occurring is p, then the probability of it not occurring is 1-p.

Help and an explanation would really be appreciated!

First one - the digits produced are independent of each other. So find the probability of each and multiply.

Probability of each digit NOT being a 0 is 0.9. so 0.9*0.9=0.81.

You can double check as the figures produced range from 00 to 99.

So 00, 01, 02, 03, 04, 05, 06, 07, 08, 09, 10, 20, 30, 40, 50, 60, 70 80 90 are not included. 19 numbers not included so 81 included.

Slashlover, thank you! That makes sense and I can explain it. Thanks again!!

Second one - not 100% sure but from the father's perspective.

Odds of winning - 0.3 (Ahmad losing)
Odds of losing - 0.1 (Ahmad winning)
Odds of draw - 0.6 (Ahmad neither winning or losing)

Probability of father not winning 0.7.

I think it's trying to catch people out into thinking that because Ahmad wins 0.1 then his father must win the other 0.9.

Ah, that makes sense too, now! Thanks again