Hi there! I have been working on this problem for quite a while and I keep getting it wrong.
A deck is shuffled and three cards are dealt.
(a) Find the chance that the first card is a king. Give your answer as a fraction.
(b) Find the chance that the first card is a king, the second is a queen, and the third is a jack. Give your answer as a decimal rounded to four decimal places.
So I keep getting half the question right. I got 4/52 for part (a) and for part be I keep getting .0029 for part (b). I am pretty positive part (a) is correct, but now I don't understand part (b) and how I keep getting the answer wrong!
Thank you so much!
a) is correct, you were just concerned about the first card, the others didn't matter
b) Prob(first card is a king) = 4/52 = 1/13
then you want a queen, but one card is gone, so 4/51
and then a Jack ----> 4/50
prob(your event) = (1/13)(4/51)(4/50) = appr .0005
Hello! I can help you understand and verify your answers for parts (a) and (b) of the problem.
For part (a), you correctly calculated the probability of getting a king as the first card. In a standard deck of 52 cards, there are 4 king cards (one in each suit). So the probability of drawing a king as the first card is 4/52, which simplifies to 1/13. Your answer of 4/52 is correct.
For part (b), you need to find the probability of drawing a king as the first card, a queen as the second card, and a jack as the third card, in that order. To calculate this probability, you need to consider that each draw is independent and the number of cards in the deck decreases after each draw.
The probability of drawing a king as the first card is still 4/52 (after which there are 51 cards remaining in the deck). The probability of drawing a queen as the second card is 4/51 (since there are 4 queen cards left in the remaining 51 cards). Finally, the probability of drawing a jack as the third card is 4/50 (as there are 4 jack cards remaining in the 50 cards left).
To find the probability of all three events happening in order, you need to multiply these individual probabilities: (4/52) * (4/51) * (4/50). This simplifies to 16/165,750.
Therefore, the probability of getting the first card as a king, the second card as a queen, and the third card as a jack is indeed 16/165,750, which can be rounded to 0.0001 as a decimal.
Please let me know if you need any further clarification or assistance!