To determine which event is the most likely to occur when Janell draws 1 card out of a standard deck of 52 cards, we have to compare the probability of each of the events:
A. The card is a face card (jack, queen, or king).
B. The card is a number card (2 through 10).
C. The card is a heart.
D. The card is an ace.
We calculate the probability of each event by dividing the number of ways the event can occur by the total number of possible outcomes (cards in the deck).
A. The Probability of Drawing a Face Card:
There are 12 face cards in the deck (4 jacks, 4 queens, and 4 kings), hence:
Probability(A) = Number of face cards / Total number of cards
Probability(A) = 12 / 52
B. The Probability of Drawing a Number Card:
Number cards include 2 through 10 in all four suits, which gives us 9 cards per suit. With four suits, that's 9*4:
Probability(B) = Number of number cards / Total number of cards
Probability(B) = 36 / 52
C. The Probability of Drawing a Heart:
There are 13 hearts in the deck (one for each rank, including both face and number cards):
Probability(C) = Number of hearts / Total number of cards
Probability(C) = 13 / 52
D. The Probability of Drawing an Ace:
There are 4 aces in the deck (one for each suit):
Probability(D) = Number of aces / Total number of cards
Probability(D) = 4 / 52
Now we compare the probabilities:
Probability(A) = 12 / 52
Probability(B) = 36 / 52
Probability(C) = 13 / 52
Probability(D) = 4 / 52
To find out the most likely event, we look for the highest probability:
We can see that Probability(B) is the highest among the four because 36 is the largest numerator:
Probability(B) = 36 / 52
Thus, the most likely event is B, Janell drawing a number card (2 through 10).
