Exercise 33.1

### A coin is tossed repeatedly until a tail comes up for the first time. Write the sample space for this experiment.

According to the question, a coin is tossed and if the outcome is tail the experiment is over. If the outcome is Head, then the coin is tossed again. If the outcome is tail, then experiment is over,...

### A coin is tossed. If it shows tail, we draw a ball from a box which contains 2 red 3 black balls; it shows head, we throw a die. Find the sample space of this experiment.

According to the question, A coin is tossed and there is box which contains 2 red and 3 black balls. When coin is tossed, the outcomes will be {H, T} According to question, if tail is turned up,...

### An experiment consists of tossing a coin and then tossing it second time if head occurs. If a tail occurs on the first toss, then a die is tossed once. Find the sample space.

According to the question, a coin is tossed and if the outcome is tail then, a die will be rolled. The possible outcome for coin is 2 that is {H, T} And, the possible outcome for die is 6 that is...

### A coin is tossed twice. If the second throw results in a tail, a die is thrown. Describe the sample space for this experiment.

According to the question, A coin is tossed twice. If the second throw results in a tail, a die is thrown. When a coin tossed twice, then sample spaces will be, {HH, TT, HT, TH} Now, according to...

### 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.

According to the question, a coin is tossed and the die is rolled. So, when coin is tossed there will be 2 events that is either Head or tail, According to question, If Head occurs on coin then Die...

### A coin is tossed and then a die is thrown. Describe the sample space for this experiment.

According to the question, a coin is tossed and then a die is thrown. So, when coin is tossed there will be 2 events, that is either Head or Tail. And, when die is thrown then there will be 6 faces...

### What is the total number of elementary events associated to the random experiment of throwing three dice together?

According to the question, three dice are thrown together. So there are 6 faces on die. As a result, the total numbers of elementary events on throwing three dice are \$6^3=216\$

### Two dice are thrown. Describe the sample space of this experiment.

As we know, there are 6 faces on a dice containing (1, 2, 3, 4, 5, 6). According to the question, two dice are thrown, so we have two faces of dice (one of each). As a result, the total sample space...

### Write the sample space for the experiment of tossing a coin four times.

According to the question, a coin is tossed four time, so the no. of samples will be, \$2^4=16\$ So, S = {HHHH, TTTT, HHHT, HHTH, HTHH, THHH, HHTT, HTTH, HTHT, THHT, THTH, TTHH, HTTT, THTT, TTHT,...

### If a coin is tossed three times (or three coins are tossed together), then describe the sample space for this experiment.

According to the question, a coin is tossed three times, so the no. of samples will be, \$2^3=8\$ So, S = {HHH, TTT, HHT, HTH, THH, HTT, THT, TTH} ∴ The sample space is {HHH, TTT, HHT, HTH, THH, HTT,...