1)Two marbles are chosen at random from a bag containing 3 blue and 2 red marbles. The relative-frequency histogram shows the distribution of the number of red marbles chosen. Find P(0 red). (the gragh shows 3/10 for 0 red, 3/5 for 1 red, and 1/10 for 2 red)
A)0
B)8/15
C)3/10
D)2/5
I chose C
2)A red die and a blue die are tossed. What is the probability that the red die shows a 3 and the blue die shows a number greater than 3?
A)1/10
B)1/5
C)1/12
D)3/5
I chose C
3)Tickets are numbered 1 to 50 and placed in a box. Three tickets are drawn at random without replacement. What is the probability that their numbers are all greater than 25?
A)1/8
B)23/196
C)69/625
D)1/2
I chose D
4)From 4 yellow and 8 blue marbles, 3 are selected. What is the probability that all 3 are yellow or all 3 are blue.
A)3/11
B)1/55
C)14/55
D)3/220
I don't know I GUESS A
5)A card is drawn from a standard deck of cards. What is P(heart or a 6)?
A)9/26
B)17/52
C)1/4
D)4/13
I chose B
5) There are 13 hearts and 3 sixes that are not hearts. You can't count the six of hearts twice. That makes 16/52. Which fraction choice is that?
1 and 2 are correct
for 3 I got 23/196
there are 25 tickets greater than 25
so prob = 25/50 x 24/49 x 23/48 = 23/196
for 4 you have to use a formula that says:
P(A or B) =P(A) + P(B) - P(A and B)
since the prob of them being 3 yellow AND 3 blue is zero
P(3yellow) = 4/12 x 3/11 x 2/10 = 1/55
P(3blue) = 8/12 x 7/11 x 6/10 = 14/55
so your prob = 1/55 + 14/55 = 3/11
GOOD GUESS
#5 (use the same formula as #4)
prob(heart) = 13/52
Prob(6) = 4/52
Prob(6of hearts) = 1/52
so prob(heart OR a 6) = 13/52 + 4/52 - 1/52
= 16/52
= 4/13
1) To find P(0 red), we look at the relative-frequency histogram. The graph shows that the probability of getting 0 red marbles is 3/10. Therefore, the answer is C) 3/10.
2) When a red die and a blue die are tossed, the outcomes are independent. The probability of the red die showing a 3 is 1/6, and the probability of the blue die showing a number greater than 3 is 2/6 (as there are 4 possibilities: 4, 5, or 6). Therefore, the probability of both events occurring is (1/6) * (2/6) = 1/18. However, the provided answer choices do not include 1/18. So, in this case, none of the answer choices are correct.
3) There are 50 tickets in total, and we are drawing 3 tickets without replacement. To find the probability that all three numbers are greater than 25, we divide the number of favorable outcomes by the number of total outcomes. The number of favorable outcomes is C(25,3) (which represents selecting 3 numbers from the 25 numbers greater than 25), and the number of total outcomes is C(50,3) (which represents selecting any 3 numbers from the 50 numbers). So, the probability is C(25,3) / C(50,3) = 1/2. Therefore, the answer is D) 1/2.
4) There are 12 marbles in total, and we are selecting 3 marbles. To calculate the probability that all 3 marbles are yellow or all 3 are blue, we have two cases to consider: (1) all 3 are yellow and (2) all 3 are blue.
For (1) all 3 are yellow: There are 4 yellow marbles, so the probability of selecting 3 yellow marbles without replacement is (4/12) * (3/11) * (2/10) = 1/55.
For (2) all 3 are blue: There are 8 blue marbles, so the probability of selecting 3 blue marbles without replacement is (8/12) * (7/11) * (6/10) = 14/55.
So, the probability of either of these cases happening is (1/55) + (14/55) = 15/55, which simplifies to 3/11. Therefore, the answer is A) 3/11.
5) In a standard deck of 52 cards, there are 13 hearts and 4 sixes. There is only one card that is both a heart and a 6 (the 6 of hearts). Therefore, the probability of drawing a heart or a 6 is (13/52) + (4/52) - (1/52) = 16/52, which simplifies to 4/13. Therefore, the answer is D) 4/13.
1) To find the probability of getting 0 red marbles, we need to consider the total number of ways we can choose 2 marbles from the bag and the number of ways we can choose 0 red marbles.
Total number of ways to choose 2 marbles from 5 (3 blue and 2 red):
C(5, 2) = 5! / (2!(5-2)!) = 10
Number of ways to choose 0 red marbles:
C(3, 0) * C(2, 2) = 1 * 1 = 1
Therefore, the probability of getting 0 red marbles is 1/10.
2) To find the probability that the red die shows a 3 and the blue die shows a number greater than 3, we need to consider the total number of outcomes and the number of favorable outcomes.
Total number of outcomes when tossing two dice:
Total outcomes = 6 (for the red die) * 6 (for the blue die) = 36
Number of favorable outcomes:
The red die showing 3 and the blue die showing a number greater than 3 can only happen when the blue die shows 4, 5, or 6 (3 possibilities).
Therefore, the probability is 3/36 = 1/12.
3) To find the probability that all three tickets drawn are greater than 25, we need to consider the total number of ways to draw three tickets and the number of ways to draw three tickets greater than 25.
Total number of ways to draw three tickets:
C(50, 3) = 50! / (3!(50-3)!) = 19600
Number of ways to draw three tickets greater than 25:
C(25, 3) = 25! / (3!(25-3)!) = 2300
Therefore, the probability is 2300/19600 = 23/196.
4) To find the probability of selecting all 3 yellow marbles or all 3 blue marbles, we need to consider the total number of ways to select 3 marbles and the number of ways to select either all yellow or all blue marbles.
Total number of ways to select 3 marbles:
C(12, 3) = 12! / (3!(12-3)!) = 220
Number of ways to select all 3 yellow marbles:
C(4, 3) = 4! / (3!(4-3)!) = 4
Number of ways to select all 3 blue marbles:
C(8, 3) = 8! / (3!(8-3)!) = 56
Therefore, the probability is (4 + 56) / 220 = 60/220 = 3/11.
5) To find the probability of drawing a heart or a 6 from a standard deck of cards, we need to consider the total number of cards in a deck and the number of favorable cards.
Total number of cards in a standard deck:
Total cards = 52
Number of favorable cards (hearts + 6):
Number of hearts = 13
Number of 6s = 4
However, we need to subtract the intersection (1 card: 6 of Hearts) to avoid double-counting:
Number of favorable cards = 13 + 4 - 1 = 16
Therefore, the probability is 16/52 = 4/13.
Based on the explanations, your answers are:
1) The probability of getting 0 red marbles is actually 1/10, not 3/10. So the correct answer is A) 0.
2) The correct answer is C) 1/12.
3) The correct answer is B) 23/196.
4) The correct answer is B) 1/55.
5) The correct answer is D) 4/13.