Question

A coin is tossed once. Then, if it comes up heads, a die is thrown once; if the coin
comes up tails, it is tossed twice more. Using the notation in which (H,2), for example,
denotes the event that the coin comes up heads and then the die comes up 2, and
(T,T,T) denotes the event the coin comes up tails three times in a row, list

(a) the 10 elements of the sample space S;
(b) the elements of S corresponding to event A that exactly one head occurs;
(c) the elements of S corresponding to event B that at least two tails occur or a
number greater than 4 occurs.

Answer 1

Using the principle of probability, the probability of the events in the question are :

• Sample space = (H1, H2, H3, H4, H5, H6, THT, TTT, HTH, HTT)

• P(A) = 4/5

• P(B) = 1/2

To obtain the sample space, take the following steps :

Coin toss = ( H, T)

Die throw = (1, 2, 3, 4, 5, 6)

First experiment :

• Coin toss (H, T)

If H : roll a die once :

• (H1, H2, H3, H4, H5, H6)

If T ; toss coin twice :

• First toss : (TH, TT)
• Second toss : (THT, TTT, HTH, HTT)

A.) The ten elements of the sample space :

• (H1, H2, H3, H4, H5, H6, THT, TTT, HTH, HTT)

B.)

Event A = exactly one head occurs

P(A) = required outcome / Total possible outcomes

P(A) = 8/10 = 4/5

C.)

Event B = atleast two tails or a number greater than 4

atleast 2 tails or number greater than 4 = 5

P(B) = 5/10 = 1/2

Therefore, the probability of event B is 0.5.

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