You pick a card at random, put it back, and then pick another card at random. 345 What is the probability of picking a 4 and then picking a 3? Write your answer as a fraction or whole number. _____

Determine total number of cards: Step 1: Determine the total number of cards in a standard deck. A standard deck has 52 cards.Calculate probability of picking 4: Step 2: Calculate the probability of picking a 4 from the deck. There are 4 cards with the number 4 in a deck (one for each suit). Probability of picking a 4 = Number of 4s / Total number of cards = 4 / 52.Calculate probability of picking 3: Step 3: Since the card is replaced, the total number of cards remains the same. Calculate the probability of picking a 3 after replacing the first card. There are also 4 cards with the number 3 in the deck. Probability of picking a 3 = Number of 3s / Total number of cards = 4 / 52.Find overall probability: Step 4: Multiply the probabilities from Step 2 and Step 3 to find the overall probability of the sequence (picking a 4 and then a 3). Overall probability = (4 / 52) * (4 / 52) = 16 / 2704.

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You pick a card at random, put it back, and then pick another card at random. $\newline$ $345$ $\newline$ What is the probability of picking a $4$ and then picking a $3$ ? $\newline$ 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, put it back, and then pick another card at random.

\newline

345

\newline

What is the probability of picking a

4

and then picking a

3

\newline

Write your answer as a fraction or whole number.

\newline

\_\_\_\_

Determine total number of cards: Step $1$ : Determine the total number of cards in a standard deck. $\newline$ A standard deck has $52$ cards.
Calculate probability of picking $4$ : Step $2$ : Calculate the probability of picking a $4$ from the deck. $\newline$ There are $4$ cards with the number $4$ in a deck (one for each suit). $\newline$ Probability of picking a $4 = \frac{\text{Number of 4s}}{\text{Total number of cards}} = \frac{4}{52}.$
Calculate probability of picking $3$ : Step $3$ : Since the card is replaced, the total number of cards remains the same. Calculate the probability of picking a $3$ after replacing the first card. $\newline$ There are also $4$ cards with the number $3$ in the deck. $\newline$ Probability of picking a $3$ = Number of $3$ s / Total number of cards = $4 / 52$ .
Find overall probability: Step $4$ : Multiply the probabilities from Step $2$ and Step $3$ to find the overall probability of the sequence (picking a $4$ and then a $3$ ). $\newline$ Overall probability = $(\frac{4}{52}) \times (\frac{4}{52}) = \frac{16}{2704}$ .