Question

3. A fair coin is flipped 4 times.

(a) What is the probability that the third flip is tails?

(b) What is the probability that we never get the same outcome (heads or tails) twice in a row?

(c) What is the probability of tails appearing on at most one of the four flips?

(d) What is the probability of tails appearing on either the first or the last flip (or both)?

(e) What is the probability of tails appearing before any heads appear?

4. Let A and B be two events in a sample space S . If the probability that at least one of them occurs is 0.3 and the probability that A occurs but B does not occur is 0.1, what is P(B)?

5. Two fair dice are tossed.

(a) What is the probability that the resulting values sum to 10 or more?

(b) What is the probability that the values appearing on the two dice are different?

Answer #1

#3.

There are total 16 possible outcomes

a)

There are 8 outcomes where 3rd flip is tail,

Hence probability = 8/16 = 1/2

b)

There are HTHT, THTH possible outcomes in this case

Required probability = 2/16 = 1/8

c)

There are 5 such outcomes

Probability = 5/16

d)

THHH, HHHT or THHT

probability = 3/16

e)

TTTT, THTT, TTHT, TTTH

probability = 4/16 = 1/4

#5.

If two dice are rolled, below are the outcomes

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

a)

There are total 36 outcomes

There are 6 outcomes for which sum is 10 or more

Probability = 6/36 = 1/6

b)

There are 30 outcomes where different values appear on the two dice

Probability = 30/36 = 5/6

Suppose a fair coin is flipped three times.
A). What is the probability that the second flip is heads?
B). What is the probability that there is at least two
tails?
C). What is the probability that there is at most two heads?

Given a fair coin, if the coin is flipped n times, what is the
probability that heads is only tossed on odd numbered tosses.
(tails could also be tossed on odd numbered tosses)

4. A fair coin is flipped 6 times.
a. what is the distribution
of outcomes?
b. what is the probability
of getting 4 heads/2 two tails in six flips of a
coin?

A coin is tossed five times. By counting the elements in the
following events, determine the probability of each event. (Show
your work)
a. Heads never occurs twice in a row.
b. Neither heads or tails occur twice in a row
c. Both heads and tails occur at least twice in a row.
The answers are 13/32, 1/16, and 1/4. I'm just stuck on how to
get them.

i
flip one fair coin until I get 4 tails( total, not in a row) or 3
heads ( total, not in a row).
(a) what is the maximum number of flips for this game?
(b) what is the probability the game requires exactly 4
flips?
(c) what is the probability the 3 heads occur before the 4
tails?
(d) what is the probability if I filp 10 fair cions at least 8
are heads?

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2
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