Hello averera

Welcome to Math Help Forum!Here's how you do 1A:

The total number of ways of choosing 3 cards from 52 isThe number of ways of choosing 1 black from 26 is 26; and the number of ways of choosing 2 red from 26 is . So the number of ways of choosing 1 black and 2 red isTherefore the probability that this occurs when 3 cards are chosen from 52 isI'm not quite sure what you mean by the 'opposite events'. Do you mean the probability that this doesn't happen? If so, then it's .

Do 1B and 1C in a similar way.

Start B by saying "The number of ways of choosing 3 reds from 26 is ..."

And start C by saying "The number of ways of choosing 1 club from 13 is 13...

Can you complete these now?

For question 2:

The number of ways of choosing 4 balls from 32 is ... ? (a)

The number of ways of choosing 2 white from 10 is ... ?

The number of ways of choosing 2 black from 12 is ... ?

So the number of ways of doing each of these things, one after the other is ... ? (b) (Hint: Multiply these two answers together.)

Therefore the probability that this occurs is ... ? (Hint: divide the second answer (b) by the first, (a).)

Can you do this one now?

Grandad

PS Here are the answers.

Spoiler: