Question

An unbiased coin is tossed 15 times.

1. Find the probability that the coin lands heads exactly 9 times. a. 0.0003 b. 0.3571 c. 0.6429 d. 0.1527 e. 0.4213

2. Find the probability that the coin lands tails at most 3 times. a. 0.0002 b. 0.0037 c. 0.5000 d. 0.0176 e. 0.8723

3. Find the probability that the coin lands heads at least 3 times. a. 0.0005 b. 0.9963 c. 0.9333 d. 0.0003 e. 0.8890

A computer stores receives a box of a certain video game. The box contains 35 games of which 4 are defective. A quality-control inspector randomly chooses 6 games from the box.

4. What is the probability that exactly 2 are defective? a. 0.0111 b. 0.0075 c. 0.1667 d. 0.8333 e. 0.1163

5. What is the probability that 0 are defective? a. 0.05410 b. 0.45361 c. 0.15473 d. 0.00029 e. 0.92445

6. What is the probability that at most 3 are defective? a. 0.9997 b. 0.6102 c. 0.5464 d. 0.8957 e. 0.2189

Carrie draws 5 cards simultaneously from a well-shuffled deck of 52 playing cards.

7. What is the probability that she chooses 3 spades and 2 cards that are not spades? a. 0.7692 b. 0.0782 c. 0.2308 d. 0.2743 e. 0.0815

8. What is the probability that she chooses 2 red face cards? a. 0.4308 b. 0.2273 c. 0.0876 d. 0.0962 e. 0.1736 Use the following problem to answer questions 9 and 10. A group of 27 people contains 13 males and 14 females. Six people are chosen at random.

9. What is the probability that 1 female is chosen? a. 0.1826 b. 0.0011 c. 0.0654 d. 0.3442 e. 0.0609

10. What is the probability that at most 1 male is chosen? a. 0.3021 b. 0.0981 c. 0.0909 d. 0.2044 e. 0.6596

Answer #1

1)

probability that the coin lands heads exactly 9
times=^{15}C_{9}(0.5)^{9}(0.5)^{6}
=0.1527

2)probability that the coin lands tails at most 3 times=0.0176

3) probability that the coin lands heads at least 3 times=0.9963

4) probability that exactly 2 are defective=0.1163

5)probability that 0 are defective=0.4536

6)probability that at most 3 are defective =0.9997

7)probability that she chooses 3 spades and 2 cards that are not spades=0.0815

8)probability that she chooses 2 red face cards=0.0876

9) probability that 1 female is chosen=0.0609

10) probability that at most 1 male is chosen=0.0981

When coin 1 is flipped, it lands on heads with probability
3
5
; when coin 2 is flipped it lands on heads with probability
4
5
.
(a)
If coin 1 is flipped 11 times, find the probability that it
lands on heads at least 9 times.
(b)
If one of the coins is randomly selected and flipped 10 times,
what is the probability that it lands on heads exactly 7
times?
(c)
In part (b), given that the...

A fair coin is tossed 4 times, what is the probability
that it lands on Heads each time?

When coin 1 is flipped, it lands on heads with probability
3/5 ; when coin 2 is flipped it lands on heads with probability
4/5 .
(a)
If coin 1 is flipped 12 times, find the probability that it
lands on heads at least 10 times.
(b)
If one of the coins is randomly selected and flipped 10 times,
what is the probability that it lands on heads exactly 7
times?
(c)
In part (b), given that the first of...

A coin is tossed 100 times and the results are recorded. 40
times the coin lands on heads, the other 60 times the coin lands on
tails. If 40 of the recorded tosses were selected at random, what
is the probability that the coin landed on heads exactly 14
times?

A fair coin is tossed 4 times, what is the probability that it
lands on Heads each time?
You have just tossed a fair coin 4 times and it landed on Heads
each time, if you toss that coin again, what is the probability
that it will land on heads?
Give examples of two independent events.
Dependent events are (sometimes, always, never) (choose one)
mutually exclusive.
If you were studying the effect that eating a healthy breakfast
has on a...

1.
two coins are tossed, find the probability that two heads are
obtained. note: each coin has two possible outcomes H (heads) and T
(tails).
2. which of these numbers cannot be a probability? why?
a) -0.00001
b) 0.5
c) 20%
d)0
e) 1
3. in a deck of 52 cards, what is the probability of drawing a
three of spades, and then a four of clubs, without
replacement?
4. what is the probability of the same outcome in #3,...

Suppose I have two biased coins: coin #1, which lands heads with
probability 0.9999, and coin #2, which lands heads with probability
0.1. I conduct an experiment as follows. First I toss a fair coin
to decide which biased coin I pick (say, if it lands heads, I pick
coin #1, and otherwise I pick coin #2) and then I toss the biased
coin twice. Let A be the event that the biased coin #1 is chosen,
B1 the event...

The theoretical probability of a coin landing heads up is
1/2
Does this probability mean that if a coin is flipped two times,
one flip will land heads up? If not, what does it mean?
Choose the correct answer below.
A.
Yes, it means that if a coin was flipped two times, at least
one of the tosses would land heads up.
B.
Yes, it means that if a coin was flipped two times, exactly
one of the tosses would...

A coin is tossed 10 times to test the hypothesis (?0) that the
probability of heads is ½ versus the alternative that the
probability is not ½. A test is defined by: reject ?0 if either 0
or 10 heads are observed.
a. What is the significance level of the test?
b. If in fact the probability of heads is 0.1, what is the
power, (1 − ?), of the test?

PROBABILITY QUESTION
A fair coin is tossed n times. Sn is the # of heads
after tossed. Show that P(Sn ≥ 3n/4) ≤ e -n/8
.

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