Help in Solving a Probability Question from an ordinary deck of 52 cards?

P(five and a jack)= 4/52 x 4/52 = 1/169

The are 4 fives and 4 jacks in a deck of cards. Therefore, they will both be 4/52. Because it says 'and', we have to multiply the two fractions because it is asking what the probability of getting both of them at the same time are.

P(heart and a jack)= 13/52 x 4/52 = 1/52

There are 13 hearts in a pack of cards. Also, there are 4 jacks in a pack of cards (same as above). Just like before, we multiply these two because it says 'and'.

I really hope this helped :)

P(five and a jack)= 2*(4/52)(4/51) = 8/663

Basic idea is that you have 52 cards, you have 4/52 shot of picking a 5 so (4/52), THEN you have 51 cards remaining in the deck so to get a jack (4/51) but remember there are 2 ways to pick a jack and a 5. First the 5 then the jack or first the jack then the 5.

P(heart and a jack)= 2(1/52) + 2*(12/52)(3/51) = (102 + 72)/(52*51) = 29/442

2 things to look at here, first is the case we draw the jack of hearts. Again 2 ways of doing it, as the first card or as the 2nd. if we choose this card, we don't care what the other card is. Otherwise, we look at the case that we don't choose the jack of hearts. So we have a 12/52 chance of picking a heart that is no also a jack. Then we have 51 cards remaining, so 3/51 to choose a jack (that isn't the jack of hearts). Again there are 2 ways of doing it.