1. A test was given to a group of students. The grades and gender are summarized in the table below.
A B C Total
Male 6 12 4 22
Female 6 14 6 26
Total 12 26 10 48
If one student is chosen at random from those who took the test, find the probability that the student was female or got a C.
a. .54
b. .63
c. .20
c. .75
2. If two cards are chosen from a standard deck of cards, what is the probability of first getting a diamond and then a club? (assume replacement of the first card)
a. 1/13 * 1/13
b. 1/13 * 1/12
c. 1/13 + 1/13
c. ¼ * ¼
there are 30 students who fit the criteria ... 26 females ... 4 males with a C
... 30 / 48 = ?
2. each suite is 1/4 of the deck
... last response looks good
1. To find the probability that the student was female or got a C, we need to sum the probabilities of each event individually and subtract the probability of their intersection (i.e., the event of being a female student who also got a C). The probability of a student being female is 26/48, and the probability of a student getting a C is 10/48. The probability of a student being both female and getting a C is given by the intersection of the female and C categories, which is 6/48.
Therefore, the probability that the student was female or got a C is (26/48) + (10/48) - (6/48) = 30/48 = 0.625.
Rounded to two decimal places, the answer is approximately 0.63.
The correct answer is b. 0.63.
2. Since there are 13 diamonds and 52 total cards in the standard deck, the probability of drawing a diamond on the first draw, assuming replacement, is 13/52 = 1/4.
Since one diamond has already been drawn and there are only 51 cards left in the deck, the probability of drawing a club on the second draw is 13/51.
Therefore, the probability of first getting a diamond and then a club is (1/4) * (13/51) = 13/204.
The correct answer is a. 1/13 * 1/13.
To solve these probability problems, we need to gather the required information and apply the appropriate formulas.
1. To find the probability that the student chosen was either female or got a C, we need to determine the total number of outcomes that fall into these categories and divide it by the total number of possible outcomes.
From the table, we can see that there are 6 female students who got a C. Additionally, there are 20 female students in total, and 10 students who got a C regardless of gender. Therefore, the total number of outcomes that fall into the female or C category is 6 + 20 - 6 (to avoid double-counting the female students who also got a C), which equals 20.
The total number of possible outcomes is given by the sum of all the values in the "Total" row, which is 48.
Therefore, the probability that the student chosen was female or got a C is 20/48, which simplifies to 5/12 or approximately 0.4167. However, none of the options provided match this value exactly. It seems there might be an error in the answer choices.
2. To find the probability of getting a diamond and then a club when two cards are chosen with replacement, we need to consider the number of favorable outcomes and divide it by the total number of possible outcomes.
In a standard deck of 52 cards, there are 13 diamonds and 13 clubs. Assuming replacement, the probability of getting a diamond on the first draw is 13/52 (or 1/4) since there are 13 diamonds out of 52 cards.
Since we are replacing the first card, when drawing again, there are still 13 clubs and a total of 52 cards. Thus, the probability of getting a club on the second draw is also 13/52 (or 1/4).
To find the probability of both events happening, we multiply these two probabilities together: (13/52) * (13/52) = 169/2704 = 1/16.
Therefore, the correct answer is a. 1/13 * 1/13, which simplifies to 1/16.