You pick a card at random, put it back, and then pick another card at random. 234 What is the probability of picking a 4 and then picking a 4? Write your answer as a fraction or whole number. _____

Counting Fours in Deck: First, let's figure out how many 4s are in a deck of cards. There are 4 suits, and each suit has one 4 card, so there are 4 fours in a deck of 52 cards. Calculate First Draw Probability: Now, calculate the probability of picking a 4 on the first draw. The probability is the number of favorable outcomes (picking a 4) divided by the total number of outcomes (total cards). So, it's 4/52, which simplifies to 1/13. Calculate Second Draw Probability: Since the card is put back in the deck, the total number of cards and the number of 4s remain the same for the second draw. So, the probability of picking another 4 is also 1/13. Find Probability of Both Events: To find the probability of both events happening (picking a 4 and then picking another 4), multiply the probabilities of the individual events. So, it's 1/13 * 1/13 = 1/169.

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You pick a card at random, put it back, and then pick another card at random. $\newline$ $234$ $\newline$ 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, put it back, and then pick another card at random.

\newline

234

\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

\_\_\_\_

Counting Fours in Deck: First, let's figure out how many $4$ s are in a deck of cards. There are $4$ suits, and each suit has one $4$ card, so there are $4$ fours in a deck of $52$ cards.
Calculate First Draw Probability: Now, calculate the probability of picking a $4$ on the first draw. The probability is the number of favorable outcomes (picking a $4$ ) divided by the total number of outcomes (total cards). So, it's $\frac{4}{52}$ , which simplifies to $\frac{1}{13}$ .
Calculate Second Draw Probability: Since the card is put back in the deck, the total number of cards and the number of $4$ s remain the same for the second draw. So, the probability of picking another $4$ is also $\frac{1}{13}$ .
Find Probability of Both Events: To find the probability of both events happening (picking a $4$ and then picking another $4$ ), multiply the probabilities of the individual events. So, it's $\frac{1}{13} \times \frac{1}{13} = \frac{1}{169}$ .