Question
g) What is the probability of picking a three given that the card is a spade?
Round answer to 3 decimal places.
Ask by Colon Griffin. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The probability of picking a three given that the card is a spade is 0.077.
Solution
-
Define the conditional probability:
The probability of picking a three given that the card is a spade is -
Calculate the numerator
:
There is only one three of spades in the deck. Hence, -
Calculate the denominator
:
There are 13 spades in the deck. Therefore, -
Compute the conditional probability:
-
Convert the fraction to a decimal and round to 3 decimal places:
Thus, the probability is
.
Answered by UpStudy AI and reviewed by a Professional Tutor
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The Deep Dive
In a standard deck of 52 playing cards, there are 13 spades. Among those, there is only one three of spades. To find the probability of picking a three given that the card is a spade, you can use the formula:
Probability = (Number of favorable outcomes) / (Total outcomes)
So, it would be
, which is approximately 0.077. Rounding to three decimal places gives you 0.077.
Now go ahead and impress your friends with your card knowledge! It’s not just about math; it’s like diving into the secret world of probabilities and finding the magic in numbers. Cards have stories, and with each shuffle, they hold endless possibilities!