You pick a card at random. Without putting the first card back, you pick a second card at random. 678 What is the probability of picking a 6 and then picking a 6? Write your answer as a fraction or whole number. _____

Calculate total number of cards: Step 1: Calculate the total number of cards in a standard deck. There are 52 cards in a deck.Determine number of 6s: Step 2: Determine the number of 6s in the deck. There are 4 sixes in a deck (one for each suit: hearts, diamonds, clubs, spades).Calculate probability of first 6: Step 3: Calculate the probability of picking the first 6. The probability of drawing a 6 on the first draw is 4 out of 52. Probability = 4/52 = 1/13Calculate probability of second 6: Step 4: Calculate the probability of picking the second 6 after the first has been drawn. After one 6 is drawn, there are 3 sixes left and 51 cards total. Probability = 3/51Multiply probabilities: Step 5: Multiply the probabilities of the two independent events. Probability of first 6 * Probability of second 6 = 1/13 * 3/51 = 3/663

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You pick a card at random. Without putting the first card back, you pick a second card at random. $\newline$ $678$ $\newline$ What is the probability of picking a $6$ and then picking a $6$ ? $\newline$ Write your answer as a fraction or whole number. $\newline$ $\_\_$

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Math Problems

Grade 7

Probability of independent and dependent events

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Q. You pick a card at random. Without putting the first card back, you pick a second card at random.

\newline

678

\newline

What is the probability of picking a

6

and then picking a

6

\newline

Write your answer as a fraction or whole number.

\newline

\_\_

Calculate total number of cards: Step $1$ : Calculate the total number of cards in a standard deck. $\newline$ There are $52$ cards in a deck.
Determine number of $6$ s: Step $2$ : Determine the number of $6$ s in the deck. $\newline$ There are $4$ sixes in a deck (one for each suit: hearts, diamonds, clubs, spades).
Calculate probability of first $6$ : Step $3$ : Calculate the probability of picking the first $6$ . $\newline$ The probability of drawing a $6$ on the first draw is $4$ out of $52$ . $\newline$ Probability = $\frac{4}{52} = \frac{1}{13}$
Calculate probability of second $6$ : Step $4$ : Calculate the probability of picking the second $6$ after the first has been drawn. $\newline$ After one $6$ is drawn, there are $3$ sixes left and $51$ cards total. $\newline$ Probability = $\frac{3}{51}$
Multiply probabilities: Step $5$ : Multiply the probabilities of the two independent events. $Probability of first 6 \times Probability of second 6 = \frac{1}{13} \times \frac{3}{51} = \frac{3}{663}$