Questions: Two cards are drawn without replacement from an ordinary deck. Find the probability that two hearts are drawn.

Two cards are drawn without replacement from an ordinary deck. Find the probability that two hearts are drawn.
Transcript text: Two cards are drawn without replacement from an ordinary deck. Find the probability that two hearts are drawn.
failed

Solution

failed
failed

Solution Steps

Hint

To solve this problem, calculate the probability of drawing a heart on the first draw, then calculate the conditional probability of drawing a second heart given that the first card drawn was a heart. Multiply these probabilities together to find the overall probability of drawing two hearts in succession without replacement.

Step 1: Calculate the Probability of Drawing a Heart on the First Draw

The total number of cards in a deck is 52, and the number of hearts is 13. The probability of drawing a heart on the first draw is given by: \[ P(\text{First Heart}) = \frac{13}{52} = 0.25 \]

Step 2: Calculate the Conditional Probability of Drawing a Heart on the Second Draw

After drawing one heart, there are now 12 hearts left and 51 cards left in total. The conditional probability of drawing a heart on the second draw given that the first card drawn was a heart is: \[ P(\text{Second Heart} \mid \text{First Heart}) = \frac{12}{51} \approx 0.2353 \]

Step 3: Calculate the Overall Probability of Drawing Two Hearts in Succession

The overall probability of drawing two hearts in succession without replacement is the product of the probabilities calculated in Steps 1 and 2: \[ P(\text{Two Hearts}) = P(\text{First Heart}) \times P(\text{Second Heart} \mid \text{First Heart}) = 0.25 \times 0.2353 \approx 0.0588 \]

Final Answer

\[ \boxed{\frac{1}{17}} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Which of the following is NOT a strategy that labor unions used to protect workers? A) persuading politicians to make labor laws B) forcing employers to give workers food C) getting benefits for hurt or sick workers D) strikes if employers would not bargain
failedAnswered
Solve for (v). [ -3 v+2=-10 v+30 ] Simplify your answer as much as possible. [ v= ]
failedAnswered
Watch the video and then solve the problem given below. Click here to watch the video. Describe how the graph of g(x)=x-4 can be obtained from one of the basic graphs. Then graph the function. Select the correct choice below and fill in the answer box to complete your choice. A. Start with the graph of y= Shift it up 4 units. B. Start with the graph of y= Shift it down 4 units. C. Start with the graph of y= Shrink it horizontally by a factor of 4 . D. Start with the graph of y= Shift it left 4 units.
failedAnswered
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the y-axis. y=36-x^2 y=0 x=4 x=6
failedAnswered
Decide whether the sampling method could result in a biased sample. Explain your reasoning. 16. On the first day of school, all of the incoming freshmen attend an orientation program. The principal wants to learn the opinions of the freshmen regarding the orientation program. He decides to ask the first 25 freshmen that he sees. 17. The manager of an apartment building wants to know if the residents are satisfied with his service. He writes each apartment number on a piece of paper and places the pieces of paper in a hat. Then he randomly chooses 10 apartment numbers and asks the residents of the 10 apartments about his service. 18. The members of the school drama club want to know how much students are willing to pay for a ticket to one of their productions. They decide that each member of the drama club should ask five of his or her friends what they are each willing to pay: