Probability Exercise 01
Question:
A coin is tossed and a die is thrown write the simple space.
Answer:

Sample space = {(Heads, 1), (Heads, 2), (Heads, 3), (Heads, 4), (Heads, 5), (Heads, 6), (Tails, 1), (Tails, 2), (Tails, 3), (Tails, 4), (Tails, 5), (Tails, 6)}

The number of elements in the sample space = 12
Question:
A coin is tossed and then a die is rolled only in case a head is shown on the coin. Describe the sample space for this experiment.
Answer:
Answer:
Step 1: The sample space for the coin toss is {Head, Tail}.
Step 2: The sample space for the die roll is {1, 2, 3, 4, 5, 6}.
Step 3: The sample space for the entire experiment is {(Head, 1), (Head, 2), (Head, 3), (Head, 4), (Head, 5), (Head, 6), (Tail, No roll)}.
Question:
One die of red colour one of white colour and one of blue colour are placed in a bag. One die is selected at random and rolled its colour and the number on its uppermost face is noted. Describe the sample space
Answer:

Sample space = {(Red, 1), (Red, 2), (Red, 3), (Red, 4), (Red, 5), (Red, 6), (White, 1), (White, 2), (White, 3), (White, 4), (White, 5), (White, 6), (Blue, 1), (Blue, 2), (Blue, 3), (Blue, 4), (Blue, 5), (Blue, 6)}

The sample space contains 18 elements, each representing a die of a particular colour with a number from 1 to 6.
Question:
Suppose 3 bulbs are selected at random from a lot. Each bulb is tested and classified as defective (D) or nondefective (N). Write the sample space of this experiment?
Answer:
Sample Space = {DDD, DDN, DND, DNN, NDD, NDN, NND, NNN}
Question:
The numbers 1,2,3 and 4 are written separately on four slips of paper. The slips are then put in a box and mixed thoroughly. A person draws two slips from the box, one after the other without replacement. Describe the following events:A= The number on the first slip is larger than the one on the second slip. B= The number on the second slip is greater than 2 C= The sum of the numbers on the two slip is 6 or 7 D= The number on the second slips is twice that on the first slip. Which pair (s) of events is (are) mutually exclusive
Answer:
A and B are mutually exclusive. C and D are mutually exclusive.
Question:
A die is thrown repeatedly until a six comes up. What is the sample space for this experiment?
Answer:
Step 1: The sample space for this experiment is a set of all possible outcomes of the experiment.
Step 2: In this case, the possible outcomes are the numbers 1, 2, 3, 4, 5, and 6.
Step 3: Therefore, the sample space for this experiment is {1, 2, 3, 4, 5, 6}.
Question:
Describe the sample space for the indicated experiment : A coin is tossed four times
Answer:
Answer:
Step 1: The sample space for the experiment is the set of all possible outcomes of the experiment.
Step 2: The possible outcomes of the experiment are: {HHHT, HTHH, THHH, HHTT, THHT, TTHH, HTTT, THTT, TTTH, TTTT}, where H = heads and T = tails.
Step 3: Therefore, the sample space for the experiment is {HHHT, HTHH, THHH, HHTT, THHT, TTHH, HTTT, THTT, TTTH, TTTT}.
Question:
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. Write the sample space for this experiment
Answer:
Step 1: List out the possible outcomes of rolling a die: 1, 2, 3, 4, 5, 6
Step 2: For each of the even numbers (2, 4, 6), list out the possible outcomes of tossing a coin once: heads, tails
Step 3: For each of the odd numbers (1, 3, 5), list out the possible outcomes of tossing a coin twice: headsheads, headstails, tailsheads, tailstails
Sample Space: {1: headsheads, headstails, tailsheads, tailstails; 2: heads, tails; 3: headsheads, headstails, tailsheads, tailstails; 4: heads, tails; 5: headsheads, headstails, tailsheads, tailstails; 6: heads, tails}
Question:
A coin is tossed. If the out come is a head a die is thrown. If the die shows up an even number the die is thrown again. What is the sample space for the experiment?
Answer:
Step 1: The sample space for the coin toss is {Head, Tail}.
Step 2: If the outcome is a Head, the sample space for the die is {1, 2, 3, 4, 5, 6}.
Step 3: If the die shows an even number, the sample space for the second throw of the die is {2, 4, 6}.
Step 4: The sample space for the experiment is the combination of all the possible outcomes of the coin toss and the die throws. Thus, the sample space is {Head, Tail} x {1, 2, 3, 4, 5, 6} x {2, 4, 6} = {Head12, Head14, Head16, Head22, Head24, Head26, Head32, Head34, Head36, Head42, Head44, Head46, Head52, Head54, Head56, Head62, Head64, Head66, Tail12, Tail14, Tail16, Tail22, Tail24, Tail26, Tail32, Tail34, Tail36, Tail42, Tail44, Tail46, Tail52, Tail54, Tail56, Tail62, Tail64, Tail66}.
Question:
2 boys and 2 girls are in Room X and 1 boy and 3 girls in Room Y Specify the sample space for the experiment in which a room is selected and then a person
Answer:
Sample space = {(Room X, Boy), (Room X, Girl), (Room Y, Boy), (Room Y, Girl)}
Question:
A coin is tossed. If the out come is a head a die is thrown. If the die shows up an even number the die is thrown again. What is the sample space for the experiment?
Answer:
Sample Space = {HH1, HH2, HH3, HH4, HH5, HH6, TH1, TH2, TH3, TH4, TH5, TH6, HT1, HT2, HT3, HT4, HT5, HT6}
Where, HH1 = Head is tossed and die shows up 1 HH2 = Head is tossed and die shows up 2 TH1 = Tail is tossed and die shows up 1 TH2 = Tail is tossed and die shows up 2 HT1 = Head is tossed and die shows up 1 again HT2 = Head is tossed and die shows up 2 again
And so on…
Question:
Describe the sample space for the indicated experiment : A coin is tossed three times
Answer:
Answer:
Step 1: The sample space for a single coin toss is {Heads, Tails}.
Step 2: The sample space for three coin tosses is {Heads, Heads, Heads}, {Heads, Heads, Tails}, {Heads, Tails, Heads}, {Tails, Heads, Heads}, {Tails, Tails, Heads}, {Tails, Heads, Tails}, {Heads, Tails, Tails}, {Tails, Tails, Tails}.
Question:
An experiment consists of recording boygirl composition of families with 2 children (i) What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births? (ii) What is the sample space if we are interested in the number of girls in the family?
Answer:
(i) The sample space is {BB, BG, GB, GG}, where B = boy and G = girl.
(ii) The sample space is {0, 1, 2}, where 0 = no girls, 1 = one girl, and 2 = two girls.
Question:
A box contains 1 red and 3 identical white balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment
Answer:
Sample Space: {(Red, White), (White, Red), (White, White)}
Question:
An experiment consists of tossing a coin and then throwing it second time if a head occurs. If a tail occurs on the first toss then a die is rolled once. Find the sample space
Answer:
Sample Space = {(H,H), (H,T), (T,1), (T,2), (T,3), (T,4), (T,5), (T,6)}
Question:
A coin is tossed If it shows a tail we draw a ball from a box which contains 2 red and 3 black balls If it shows head we throw a die Find the sample space for this experiment
Answer:
Step 1: List the possible outcomes of tossing a coin: Head or Tail
Step 2: List the possible outcomes of drawing a ball from a box containing 2 red and 3 black balls: 2 Red Balls, 3 Black Balls
Step 3: List the possible outcomes of throwing a die: 1, 2, 3, 4, 5, 6
Step 4: Construct the sample space for this experiment: {Head2 Red Balls, Head3 Black Balls, Tail2 Red Balls, Tail3 Black Balls, Head1, Head2, Head3, Head4, Head5, Head6, Tail1, Tail2, Tail3, Tail4, Tail5, Tail6}