You pick a card at random. Without putting the first card back, you pick a second card at random. 5678 What is the probability of picking a 6 and then picking a 5? 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 probability of picking: Step 2: Determine the probability of picking a 6 first. There are 4 sixes in a deck of 52 cards. Probability of first picking a 6 = 4/52.Calculate probability of picking: Step 3: Calculate the probability of picking a 5 next, without replacing the first card. After picking a 6, there are 51 cards left, including 4 fives. Probability of then picking a 5 = 4/51.Multiply probabilities to find overall: Step 4: Multiply the probabilities from Step 2 and Step 3 to find the overall probability. Probability of picking a 6 and then a 5 = (4/52) * (4/51).Simplify the probability expression: Step 5: Simplify the probability expression. (4/52) * (4/51) = 16/2652. This simplifies to 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. $\newline$ $5678$ $\newline$ What is the probability of picking a $6$ and then picking a $5$ ? $\newline$ 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

5678

\newline

What is the probability of picking a

6

and then picking a

5

\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 probability of picking: Step $2$ : Determine the probability of picking a $6$ first. $\newline$ There are $4$ sixes in a deck of $52$ cards. $\newline$ Probability of first picking a $6 = \frac{4}{52}$ .
Calculate probability of picking: Step $3$ : Calculate the probability of picking a $5$ next, without replacing the first card. $\newline$ After picking a $6$ , there are $51$ cards left, including $4$ fives. $\newline$ Probability of then picking a $5 = \frac{4}{51}$ .
Multiply probabilities to find overall: Step $4$ : Multiply the probabilities from Step $2$ and Step $3$ to find the overall probability. $\newline$ Probability of picking a $6$ and then a $5 = \left(\frac{4}{52}\right) * \left(\frac{4}{51}\right)$ .
Simplify the probability expression: Step $5$ : Simplify the probability expression. $\newline$ $(\frac{4}{52}) \times (\frac{4}{51}) = \frac{16}{2652}$ . $\newline$ This simplifies to $\frac{4}{663}$ .