You pick a card at random. Without putting the first card back, you pick a second card at random. 1234 What is the probability of picking a 4 and then picking a 3? Write your answer as a fraction or whole number. _____

Calculate total cards: Step 1: Calculate the total number of cards in a standard deck. A standard deck has 52 cards.Determine probability of 4: Step 2: Determine the probability of picking a 4 first. There are 4 cards with the number 4 in the deck. Probability of first picking a 4 = Number of 4s / Total number of cards = 4 / 52.Calculate probability of 3: Step 3: Calculate the probability of picking a 3 next, without replacing the first card. After picking a 4, there are 51 cards left. There are still 4 cards with the number 3. Probability of picking a 3 next = Number of 3s / Remaining number of cards = 4 / 51.Find combined probability: Step 4: Find the combined probability of both events happening in sequence. Multiply the probabilities from Step 2 and Step 3. Combined probability = (4 / 52) * (4 / 51) = 16 / 2652.Simplify fraction: Step 5: Simplify the fraction obtained in Step 4. 16 / 2652 can be simplified by dividing both numerator and denominator by their greatest common divisor, which is 4. Simplified probability = 4 / 663.

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You pick a card at random. Without putting the first card back, you pick a second card at random. $\newline$ $1234$ $\newline$ What is the probability of picking a $4$ and then picking a $3$ ? Write your answer as a fraction or whole number. $\newline$ _____

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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

1234

\newline

What is the probability of picking a

4

and then picking a

3

? Write your answer as a fraction or whole number.

\newline

_____

Calculate total cards: Step $1$ : Calculate the total number of cards in a standard deck. $\newline$ A standard deck has $52$ cards.
Determine probability of $4$ : Step $2$ : Determine the probability of picking a $4$ first. $\newline$ There are $4$ cards with the number $4$ in the deck. $\newline$ Probability of first picking a $4 = \frac{\text{Number of 4s}}{\text{Total number of cards}} = \frac{4}{52}.$
Calculate probability of $3$ : Step $3$ : Calculate the probability of picking a $3$ next, without replacing the first card. $\newline$ After picking a $4$ , there are $51$ cards left. There are still $4$ cards with the number $3$ . $\newline$ Probability of picking a $3$ next = Number of $3$ s / Remaining number of cards = $4 / 51$ .
Find combined probability: Step $4$ : Find the combined probability of both events happening in sequence. $\newline$ Multiply the probabilities from Step $2$ and Step $3$ . $\newline$ Combined probability = $(\frac{4}{52}) \times (\frac{4}{51}) = \frac{16}{2652}$ .
Simplify fraction: Step $5$ : Simplify the fraction obtained in Step $4$ . $\newline$ $16 / 2652$ can be simplified by dividing both numerator and denominator by their greatest common divisor, which is $4$ . $\newline$ Simplified probability = $4 / 663$ .