help on math please...

Test Preparation SAT Preparation
1
  1. A coin is tossed four times. What is the probability of getting four heads? (answer in fraction form)
  2. A card is drawn from a standard deck of 52 cards. Find the probability of each of the following events occurring: (fraction form)
    a) The card is a club.

b) The card is a five (5).

c) The card is not a face card.

  1. The probability that a DVD player will malfunction before its warranty expires is 32%. What is the probability that the DVD player will NOT malfunction before its warranty expires? (percentage form)

  2. A family has four children. Find the probability that at least two are girls.
    (fraction form or two decimal)

  3. Given a 13-card bridge hand has been dealt from a standard deck of 52 cards, what is the probability of having

a) exactly 6 hearts?

b) exactly 7 hearts, three diamonds, two clubs, and one spade?

three decimals

2

@MITer94

3

Really?

  1. 1/2 x 1/2 x 1/2 x 1/2 = you can do that part
    2a) there are four suits so 1/4

You can do the rest. Seriously.

4

@AboutTheSame . The first 3 question are easy. I’m having trouble with 4 and 5. I got 68.75 % for 4 but not sure how to do 5

5

@zxcvbnm12161 just count the # of hands with exactly 6 hearts. Choose 6 hearts out of 13. Now you have 7 cards left to fill that are non-hearts. How many ways can you fill the remaining 7?

6

@MITer94 Thanks for your responses as always. How do you count the # of hands with exactly 6 hearts?

7

39 choose 7 for remaining 7 cards and 13 choose 6 for hearts but not sure what to do with the numbers to get the answer

8

would it be (13 choose 6 x 39 choose 7) / (52 choose 6)

9

@zxcvbnm12161 check your denominator.

10

@MITer94 it is 52 choose 13

11

@MITer94 How would I do b)?

12

@zxcvbnm12161 b) is very similar to a).

13

@MITer94 . Would it be (13 choose 7 x 13 choose 3 x 13 choose 2 x 13 choose 1) /(52 choose 13)

14

@zxcvbnm12161 yeah

15

thanks @MITer94

16

The odds of one heart = 1/52
The odds of a second heart = 1/51
How to factor in the 13-card hand (and whether it even matters) escapes me. Sorry. It’s been 45 years since I had to do SAT questions.

17

thanks @AboutTheSame

18

^ I don’t think I did much, except to demonstrate my own stupidity relative to those who actually know how to answer that type of question, but if it helped, I’m glad to have been of service. :-h