- In a normal pack of cards, write down the odds against picking each card.

a) a diamond
b) a jack
c) a red 10
d) a black picture card
e) a picture card

1. A die is rolled 3 times. Estimate the chance of 2 or 3 no.'s being the same. Find the probability that
i) the three nos are the same.
ii) the second roll is different from the first one.
iii) the three nos are all diferent
iv) two or three nos are the same

4. A huge container of lollies is all the same shape but has 10 different colours. There are exactly the same no. of lollies of each colour and thousands of each type. If 1 lolly is picked, the probability that it a particular colour is 1/10 and because there are thousands of lollies, the probability that the second is the same colour is also 1/10.
If 4 lollies are picked out, find the probability that
a) all four are diferent colours
b) any two of them are the same colour

- If 3 people are asked what day of the week they were born, find the probability that
a) 2 or 3 are the same.
b) only 2 people are the same.

- If 4 people are asked what day of the week they were born, find the probability that 2 or more people are born on the same day.

Using this idea, how many people need to be asked for their birthdate in order that at least two people sharing their birthdate will have a chance of 1/2.

The probability that my bus will arrive on time at school on any given morning is 9/10 . If I go to school 5 days a week, and there are 8 weeks in this term, how many times can I expect my bus to be late?

We do not do your homework for you. However, I will start you out. Read the questions carefully.

There are 13 diamonds in a deck of 52 cards. For the odds against a diamond:

(52-13)/52 = ?

I hope this helps.

a) To find the odds against picking each card, we need to determine the number of favorable outcomes (cards we want to pick) and the number of total outcomes (total cards in the deck).

a) There are 13 diamonds in a deck of 52 cards. So, the odds against picking a diamond would be 39:13 or simplified as 3:1.

b) There are 4 jacks in a deck of 52 cards. So, the odds against picking a jack would be 48:4 or simplified as 12:1.

c) There are 26 red cards in a deck of 52 cards, which includes both diamonds and hearts. So, the odds against picking a red 10 would be 26:1.

d) There are 3 black picture cards (jack, queen, and king) in each suit. Since there are 2 black suits (clubs and spades), the total number of black picture cards is 3 * 2 = 6. So, the odds against picking a black picture card would be 46:6 or simplified as 23:3.

e) There are 3 picture cards (jack, queen, and king) in each suit. Since there are 4 suits, the total number of picture cards is 3 * 4 = 12. So, the odds against picking a picture card would be 40:12 or simplified as 10:3.

2. To estimate the chance of 2 or 3 numbers being the same when rolling a die 3 times, we need to calculate the probabilities for different scenarios.

i) The probability that all three numbers are the same is found by calculating the probability of getting the same number on the first roll (1/6) and then multiplying it by the probability of getting the same number on the second roll (1/6) and third roll (1/6). So, the probability is (1/6) * (1/6) * (1/6) = 1/216.

ii) The probability that the second roll is different from the first one is the complement of the probability that the second roll is the same as the first one. So, it is 1 - (1/6) = 5/6.

iii) The probability that all three numbers are different is found by calculating the probability of getting a different number on the second roll (5/6) and then multiplying it by the probability of getting a different number on the third roll (4/6, since there are 4 remaining numbers after the first roll). So, the probability is (5/6) * (4/6) = 20/36 = 5/9.

iv) The probability that two or three numbers are the same is the complement of the probability that all three numbers are different. So, it is 1 - 5/9 = 4/9.

3. In a container of lollies with 10 different colors, the probability of picking a specific color is 1/10. The probability of picking the same color again is also 1/10. We need to find the probability of different scenarios when picking 4 lollies.

a) The probability that all four lollies are different colors is found by multiplying the probabilities of picking a different color each time. So, it is (1/10) * (9/10) * (8/10) * (7/10) = 3024/10000 = 0.3024.

b) The probability that any two of them are the same color is the complement of the probability that all four lollies are different colors. So, it is 1 - 0.3024 = 0.6976.

4. If 3 people are asked about their birthdates, the probability of 2 or 3 people having the same birthdate can be calculated using the concept of the complement.

a) To find the probability that 2 or 3 people have the same birthdate, we need to find the probability that all 3 people have different birthdates (which is the complement of the desired probability) and subtract it from 1. Assuming people have an equal chance of being born on any day of the week, the probability that all 3 people have different birthdates is (6/7) * (5/7) = 30/49. So, the probability that 2 or 3 people have the same birthdate is 1 - 30/49 = 19/49.

b) The probability that only 2 people have the same birthdate is the probability that at least 2 people have the same birthdate minus the probability that all 3 people have the same birthdate. So, it is 19/49 - 1/49 = 18/49.

5. If 4 people are asked about their birthdate, we can use the same reasoning as in the previous question to find the probability that 2 or more people are born on the same day.

Assuming people have an equal chance of being born on any day of the week, the probability that all 4 people have different birthdates is (6/7) * (5/7) * (4/7) = 120/343. So, the probability that 2 or more people are born on the same day is 1 - 120/343 = 223/343.

6. The birthday problem is a famous probability puzzle. To find the number of people needed for at least two people sharing their birthdate to have a chance of 1/2, we need to calculate the probability of everyone having different birthdates and subtract it from 1 until we reach a probability of 1/2.

For 1 person, the probability of having a different birthdate is 1 (since there is no one else).

For 2 people, the probability of having a different birthdate is 1 - 1/365 (assuming a non-leap year).

For 3 people, the probability of having a different birthdate is 1 - (1/365) * (1 - 1/365).

We continue this process until we find a probability of 1/2. The number of people needed will vary based on leap years, but typically it is around 23-25 people.

7. If the probability of your bus arriving on time is 9/10, the probability of it being late is 1 - 9/10 = 1/10.

If you go to school 5 days a week for 8 weeks, the total number of days is 5 * 8 = 40.

To find the expected number of times your bus will be late, we multiply the total number of days (40) by the probability of it being late (1/10). So, the expected number of times your bus will be late is 40 * 1/10 = 4. Therefore, you can expect your bus to be late 4 times.