Can some one please help me with this 3 problems I have a hard time with probabilities I'm studying for my mid-term. Thank you

1) Urn A has balls numbered 1 through 7. Urn B has balls numbered 1 through 5. A ball is selected at random from urn A and then a ball is selected at random from urn B. What is the probability that a 4 is drawn from A followed by a 2 from B?

2)Mark can remember only the first 5 digits of his friend’s phone number. He also knows that the number has 7 digits and that the last digit is not a 0. If Mark were to dial all of the possible numbers and if it takes him 20 seconds to try each one, how long would it take to try every possibility?

3) A contractor is considering a sale that promises a profit of $20,000 with a probability of .7 or a loss (due to bad weather, strikes, and such) of $3,000 with a probability of .3. What is the expected profit?

this is what i got from the 2nd problem

of the total 7 digits in the number he knows the first 5 that leaves 2 for him to find out with 0 not being the last number so he knows 10 possible for the 6th and 9 possible for the 7th (not 0) 10 * 9 = 90 possible numbers
then it takes 20 seconds to try each one so 90 * 20 = 1800 seconds = 30 minutes

I'm I correct?

#3 I got this answer

(20000*.7)-(3000*.3)
=14000-900
=$13,100. expected profit

Is this right

Ok so I really need help with problem 1 I have no clue

correct on 2.

correct on 3.
1) what is 1/7 * 1/5 ?

So the answer for #1 is 1/35 is that I have to do for that problem though?

This is how it works.

To draw a 4 out of 7 balls, you have 1 success out of 7 possible events.
To draw a 2 out of 5 balls, you have 1 success out of 5 events possible.
For both of them to happen, you use the rule of multiplication.
See also:
http://www.jiskha.com/display.cgi?id=1252450211

Sure, I can help you with these probability problems. Let's go through each one step by step and calculate the probabilities.

1) Probability of drawing a 4 from Urn A:

In Urn A, there are 7 total balls numbered 1 through 7. Since we are interested in the probability of drawing a 4, and there is only one ball with the number 4, the probability is 1/7.

2) Probability of drawing a 2 from Urn B:

In Urn B, there are 5 total balls numbered 1 through 5. Similarly, since we are interested in the probability of drawing a 2, and there is only one ball with the number 2, the probability is 1/5.

To find the probability of drawing a 4 from A followed by a 2 from B, we multiply the individual probabilities together:

Probability = (1/7) * (1/5) = 1/35

So, the probability that a 4 is drawn from A followed by a 2 from B is 1/35.

2) Finding the number of possibilities:

Mark knows the first 5 digits of his friend's phone number, and he needs to find the last 2 digits. He knows that the last digit is not a 0.

The first 5 digits can be any number from 0 to 9 (10 possibilities for each digit). The last digit, however, cannot be 0 (9 possibilities).

Therefore, the total number of possibilities is:

Total number of possibilities = 10 * 10 * 10 * 10 * 10 * 9 * 1 = 90,000

3) Expected profit:

The expected profit is calculated by multiplying each possible profit by its corresponding probability, and then summing up the products.

Expected profit = (Profit1 * Probability1) + (Profit2 * Probability2) + ...

Expected profit = ($20,000 * 0.7) + (-$3,000 * 0.3)

Expected profit = $14,000 + (-$900)

Expected profit = $13,100

So, the expected profit is $13,100.

I hope this helps you with your mid-term preparation. If you have any additional questions, feel free to ask!