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