Question

Sorry if the photo is bad :)

Answer 1

So, before solving further, let's recall that, a deck of card have 52 cards, with 26 black cards, and 26 red cards, out of which, let's first consider red cards,so 13 of 26 are heart, and the other 13 out of 26 is diamond, now let's consider the black cards, so 13 of 26 black cards are spades and the other 13 out of 26 black cards are clubs, every type have an ace card, and 9 cards numbering from 2-10 and three face cards naming, queen, king and Jack. And the probability of any event is defined as the ratio of no. of favourable outcomes to Total no. of possible outcomes, so let's stary solving all the parts one by one :

7)
`{:\implies \quad \sf P(Red\:\:card)=(26)/(52)}`

`{:\implies \quad \boxed{\bf{P(Red\:\:card)=\frac12}}}`

8)
`{:\implies \quad \sf P(Jack\:\:of\:\:diamonds)=(1)/(52)}`

`{:\implies \quad \boxed{\bf{P(Jack\:\:of\:\:diamonds)=(1)/(52)}}}`

9)
`{:\implies \quad \sf P(Ace)=(4)/(52)}`

`{:\implies \quad \boxed{\bf{P(Ace)=(1)/(13)}}}`

10)
`{:\implies \quad \sf P(A\:\:black\:\:10)=(2)/(52)}`

`{:\implies \quad \boxed{\bf{P(A\:\:black\:\:10)=(1)/(26)}}}`

11)
`{:\implies \quad \sf P(A\:\:heart)=(13)/(52)}`

`{:\implies \quad \boxed{\bf{P(A\:\:heart)=\frac14}}}`

12)
`{:\implies \quad \sf P(Not\:\:a\:\:club)=(39)/(52)}`

`{:\implies \quad \boxed{\bf{P(Not\:\:a\:\:club)=\frac34}}}`