You pick a card at random. Without putting the first card back, you pick a second card at random. 4567 What is the probability of picking a 4 and then picking a 4? 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 4s: Step 2: Determine the number of 4s in the deck. There are 4 cards of each rank in a deck, including the 4s.Calculate probability of first 4: Step 3: Calculate the probability of picking the first 4. The probability of drawing a 4 on the first draw is 4 out of 52. Probability = 4/52 = 1/13Calculate probability of second 4: Step 4: Calculate the probability of picking the second 4 after the first has been drawn. After one 4 is drawn, there are 3 4s left and 51 cards total. Probability = 3/51Multiply probabilities to find overall probability: Step 5: Multiply the probabilities of the two events to find the overall probability. Probability of first event × Probability of second event = 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. $\newline$ $4567$ $\newline$ What is the probability of picking a $4$ and then picking a $4$ ? $\newline$ 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

4567

\newline

What is the probability of picking a

4

and then picking a

4

\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 $4$ s: Step $2$ : Determine the number of $4$ s in the deck. $\newline$ There are $4$ cards of each rank in a deck, including the $4$ s.
Calculate probability of first $4$ : Step $3$ : Calculate the probability of picking the first $4$ . $\newline$ The probability of drawing a $4$ on the first draw is $4$ out of $52$ . $\newline$ Probability = $\frac{4}{52} = \frac{1}{13}$
Calculate probability of second $4$ : Step $4$ : Calculate the probability of picking the second $4$ after the first has been drawn. $\newline$ After one $4$ is drawn, there are $3$ $4$ s left and $51$ cards total. $\newline$ Probability = $\frac{3}{51}$
Multiply probabilities to find overall probability: Step $5$ : Multiply the probabilities of the two events to find the overall probability. $\newline$ Probability of first event $\times$ Probability of second event = $\frac{1}{13} \times \frac{3}{51} = \frac{3}{663}$