Answer to Question #257821 in Statistics and Probability for moni

Question

Q_2: = 2.5 An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Using the notation 4H, for example, to denote the outcome that the die comes up 4 and then the coin comes up heads, and 3HT to denote the outcome that the die comes up 3 followed by a head and then a tail on the coin, construct a tree diagram to show the elements of the sample space S. (1) List the elements corresponding to the Event-A that a number less than 3 occurs on the die (2) List the elements corresponding to the Event-B that two tails occur (3) List the elements corresponding to the Event (4) List the elements corresponding to the Event ∩B (5) List the elements corresponding to the Event A ⋃ B

Answer 1

1)

A={1HT, 1TH, 1HH, 1TT, 2H, 2T}

2)

number on the die:

B={1TT, 3TT, 5TT}

3)

A'={3HT, 3TH, 3HH, 3TT, 4H, 4T, 5HT, 5TH, 5HH, 5TT, 6H, 6T}

4)

$A'\cap B=\{3TT,5TT\}$

5)

$A\cup B=\{1HT, 1TH, 1HH, 1TT, 2H, 2T, 3TT, 5TT\}$