ming has a standard 52 - card deck. a standard 52 - card deck has 4 suits (♠, ♣, ♦, and ♥) and an equal…

ming has a standard 52 - card deck. a standard 52 - card deck has 4 suits (♠, ♣, ♦, and ♥) and an equal number of cards of each suit. she is going to randomly draw a card from the deck 300 times, putting the card back in the deck after each draw. complete the following statement with the best prediction. ming will draw something other than a ♥... choose 1 answer: a exactly 150 times b close to 150 times but probably not exactly 150 times c exactly 225 times d close to 225 times but probably not exactly 225 times

ming has a standard 52 - card deck. a standard 52 - card deck has 4 suits (♠, ♣, ♦, and ♥) and an equal number of cards of each suit. she is going to randomly draw a card from the deck 300 times, putting the card back in the deck after each draw. complete the following statement with the best prediction. ming will draw something other than a ♥... choose 1 answer: a exactly 150 times b close to 150 times but probably not exactly 150 times c exactly 225 times d close to 225 times but probably not exactly 225 times

Answer

Explanation:

Step1: Calculate probability of non - heart

In a 52 - card deck, there are 13 hearts and 52 - 13 = 39 non - hearts. The probability of drawing a non - heart in a single draw is $p=\frac{39}{52}=\frac{3}{4}$.

Step2: Calculate expected number of non - heart draws

If the experiment is repeated $n = 300$ times, the expected number of non - heart draws is $E=np$. Substituting $n = 300$ and $p=\frac{3}{4}$, we get $E=300\times\frac{3}{4}=225$. However, this is just an expected value. In a random experiment, we expect the result to be close to the expected value but not exactly equal to it due to randomness.

Answer:

D. Close to 225 times but probably not exactly 225 times