If one card is randomly picked from a standard deck of 52 cards, the probability that the card will be a number from 2 through 10, or a Heart, or both, is:
a. 51.9% (27/52)
b. 69.2% (36/52)
c. 76.9% (40/52)
d. 94.2% (49.52)
76.9% (40/52)
To calculate the probability, we need to determine the number of favorable outcomes (cards that are a number from 2 through 10 or a Heart or both) and the total number of possible outcomes (the total number of cards in the deck).
Number of favorable outcomes:
There are 9 number cards from 2 through 10 (2, 3, 4, 5, 6, 7, 8, 9, and 10), 13 Hearts, and 3 cards that are both a number from 2 through 10 and a Heart (2 of Hearts, 3 of Hearts, and 10 of Hearts). So, the number of favorable outcomes is 9 + 13 + 3 = 25.
Total number of possible outcomes:
There are 52 cards in a standard deck.
Probability:
The probability is given by the formula: favorable outcomes / total outcomes.
Therefore, the probability is 25/52 or approximately 0.4808.
So, the correct answer is not listed.
To find the probability that the card chosen is a number from 2 through 10 or a Heart or both, we need to determine the number of favorable outcomes (cards that meet the criteria) and divide it by the total number of possible outcomes (all the cards in the deck).
First, let's determine the number of cards that are numbers from 2 through 10 or Hearts. There are 9 number cards from 2 through 10 in each suit (4 suits in total), which gives us a total of 36 number cards. Additionally, there are 13 Heart cards.
Now, let's calculate the probability:
Total number of favorable outcomes = Number of number cards (36) + Number of Heart cards (13) - Number of number cards that are also Hearts (9)
= 36 + 13 - 9
= 40
Total number of possible outcomes = Total number of cards in the deck (52)
Probability = Favorable outcomes / Total outcomes
= 40 / 52
≈ 0.769
Therefore, the probability that the card will be a number from 2 through 10, or a Heart, or both is approximately 76.9%.
The correct answer is c. 76.9% (40/52).