Three cards are drawn at random from a pack of well shuffled 52 cards. Find the probability that
(i) all the three cards are of the same suit;
(ii) one is a king, the other is a queen and the third a jack.
(i) all the three cards are of the same suit;
(ii) one is a king, the other is a queen and the third a jack.
P=1252⋅851⋅450=384132600=165525≈0.29%
I am making the assumption that a card, once drawn, will not be returned to the deck prior to the next draw. However, if cards are returned, the same logic that I am about to outline would still apply only the second and third probabilities would be different, as we would always be choosing from 52 cards.
You have a standard deck of 52 shuffled cards in front of you. You randomly chose one card. There were 52 cards to choose from and there were 4 aces plus 4 kings plus 4 jacks (12 cards) that could turn that would be compatible with the goal. So, the probability of the first draw being successful would be 12 in 52.
It doesn't matter whether an ace a king or a jack was drawn on the first draw, your goal will still be maintainable. Just for the sake of argument, suppose that a jack was drawn on the first draw. Now, for the second draw, there would be 4 aces and 4 kings (8 cards) that could turn that would be compatible with the goal and there would be 51 cards to choose from. So, the probability of the second draw being successful would be 8 in 51.
Obviously, whether an ace or a king turned on the second draw, on the third and final draw there would be only 4 cards left in the deck the could turn to complete the goal and there would be 50 cards to choose from. So, the probability of the third draw being successful would be 4 in 50.
Now, we need only multiply the three probabilities together to get the sought-after probability.
P=1252⋅851⋅450=384132600=165525≈0.29%
I am making the assumption that a card, once drawn, will not be returned to the deck prior to the next draw. However, if cards are returned, the same logic that I am about to outline would still apply only the second and third probabilities would be different, as we would always be choosing from 52 cards.
You have a standard deck of 52 shuffled cards in front of you. You randomly chose one card. There were 52 cards to choose from and there were 4 aces plus 4 kings plus 4 jacks (12 cards) that could turn that would be compatible with the goal. So, the probability of the first draw being successful would be 12 in 52.
It doesn't matter whether an ace a king or a jack was drawn on the first draw, your goal will still be maintainable. Just for the sake of argument, suppose that a jack was drawn on the first draw. Now, for the second draw, there would be 4 aces and 4 kings (8 cards) that could turn that would be compatible with the goal and there would be 51 cards to choose from. So, the probability of the second draw being successful would be 8 in 51.
Obviously, whether an ace or a king turned on the second draw, on the third and final draw there would be only 4 cards left in the deck the could turn to complete the goal and there would be 50 cards to choose from. So, the probability of the third draw being successful would be 4 in 50.
Now, we need only multiply the three probabilities together to get the sought-after probability.
