Which pair has equally likely outcomes? List the letters of the two choices below which have equal probabilities of success, separated by a comma. A standard deck of cards has 12 face cards and four Aces (Aces are not face cards).
A. drawing a red seven out of a standard 52 card deck given it’s not a face card or an Ace.
B. drawing a five out of a standard 52 card deck given it’s not a face card or an Ace.
C. rolling a sum of 4 on two fair six sided dice
D. rolling a sum of 5 on two fair six sided dice
E. rolling a sum of 7 on two fair six sided dice
I am so lost....please help!
P(B)=P(D)=4/36
SO IT WOULD BE B AND D?
yes
To determine which pair has equally likely outcomes, we need to calculate the probabilities of each event in the given options.
A. Drawing a red seven out of a standard 52-card deck given it's not a face card or an Ace:
To calculate this probability, we need to know the number of red sevens in the deck. There are two red sevens in a deck: the seven of hearts and the seven of diamonds. Since there are 52 cards in total, the probability of drawing a red seven is 2/52.
B. Drawing a five out of a standard 52-card deck given it's not a face card or an Ace:
To calculate this probability, we need to know the number of fives in the deck. There are four fives in a deck: the five of hearts, diamonds, clubs, and spades. Using the same reasoning as above, the probability of drawing a five is 4/52.
C. Rolling a sum of 4 on two fair six-sided dice:
To calculate this probability, we need to count the number of ways we can achieve a sum of 4. Possible combinations are: (1, 3), (2, 2), and (3, 1). There are three possible combinations, and each die has six sides, so the probability of rolling a sum of 4 is 3/36 or 1/12.
D. Rolling a sum of 5 on two fair six-sided dice:
Similar to the previous case, we need to count the number of ways to achieve a sum of 5. Possible combinations are: (1, 4), (4, 1), (2, 3), and (3, 2). There are four possible combinations, so the probability is 4/36 or 1/9.
E. Rolling a sum of 7 on two fair six-sided dice:
To calculate this probability, we need to count the number of ways to achieve a sum of 7. Possible combinations are: (1, 6), (6, 1), (2, 5), (5, 2), (3, 4), and (4, 3). There are six possible combinations, leading to a probability of 6/36 or 1/6.
Comparing the probabilities, we can see that option E has the highest probability of occurring, followed by option C, then option B, and finally option A. Therefore, the pair with equally likely outcomes is C and B.