# Probabilities (Math)

An experiment consists of tossing a coin 14 times.
(a) How many different outcomes are possible?
(b) How many different outcomes have exactly 9 heads?
(c) How many different outcomes have at least 2 heads?
(d) How many different outcomes have at most 10 heads?

1. 👍
2. 👎
3. 👁
1. a) each turn could be 2 ways, so 2^14 = 16384

b) this is the same as asking, "in how many ways can we arrange 9 H's and 5 T's, the H's and T's are indistinguishable.

number of ways = 14!/(9!5!) = 2002

c)at least two heads implies we don't want 0 heads, or 1 head, let's find those two
1 head -----> 14!/13! = 14
so at least 2 heads = 16384 - 14 - 1 = 16369

which are 14!/(11!3!) + 14!/(12!2!) + 14!/(13!1!) + 1
= 364 + 91 + 14 + 1 = 470

so at most 10 heads = 16384 - 470 = 15914

1. 👍
2. 👎

## Similar Questions

1. ### Math

1. Suppose you spin the spinner once. Find the probability. R, R, R, R, B, B, G, Y P(yellow) A. 1/8*** B. 1/6 C. 1/4 D. 1/2 2. Suppose you spin the spinner once. Find the probability. R, R, R, R, B, B, G, Y P(red or blue) A. 0 B.

2. ### Math

If you make a tree diagram and then list all of the possible outcomes for flipping a coin and rolling a 6-sided die, how many possible outcomes are there? A) 2 B) 6 C) 12 D) 36

3. ### Statistics

An experiment consists of tossing a fair coin twice. The student reasons that there are three possible outcomes: two heads, one head and one tail, or two tails. Thus,P(HH) 1/3

4. ### Prealgebra/probability

A coin is tossed three times. Use a tree diagram to find the number of possible outcomes that could produce exactly two heads. I don't know how to write out a tree diagram on here, but I think this one is heads -> heads, tails ->

1. ### Math

Use the fundamental counting principle to find the total number of outcomes in each situation. 1.Rolling two number cubes and tossing one coin. = Is the outcome = 4? 2.Choosing from 3 sizes of distilled,filtered, or spring water.

2. ### Statistics

An Experiment consists of flipping a fair coin once and rolling a fair die once. what is the probability of observing a hear or six?

3. ### Math

A spinner has 4 equal sections: red, white, blue, and green. john spins the spinner and tosses a coin. which shows the sample space for spinning the spinner and tossing the coin? I have a chart but I cant figure out how to get

4. ### statistics

If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What is the probability of getting at least two tails? A. 1/2 B. 2/3 C. 3/4 D. 4/9 mY ANSWER IS A

1. ### Physics

A coin is placed on a large disk which rotates uniformly at a rate of 2 rot/s. The coefficient of friction between the coin and the disk is 0.1. To what distance from the center of the disk should the coin be placed so that the

2. ### Math

Alice has two coins. The probability of Heads for the first coin is 1/4, and the probability of Heads for the second is 3/4. Other than this difference, the coins are indistinguishable. Alice chooses one of the coins at random and

3. ### finite math

A probability experiment was conducted in which the sample space of the experiment is S={1,2,3,4,5,6,7,8,9,10,11,12}, event F= {3,6,7,}, and event G={9,10,12}. Assume that each outcome is equally likely. List the outcomes of F and

4. ### Mathematics

A coin (H: heads; T: tails) is flipped and a number cube (1, 2, 3, 4, 5, 6) is rolled. List all the favorable outcomes for the event "rolling an even number." What is the probability of rolling an even number for this experiment?