Probability

### A fair die is rolled. Consider events and . Find (i) and (ii) and (iii) and Solution: The sample space for the given event is $S={1,2,3,4,5,6}$ Sample space of events,$E={1,3,5}, F={2,3}$ and $G={2,3,4,5} \ldots \ldots \ldots$ (i)The events probability of events are:...

### A black and a red dice are rolled.(a) Find the conditional probability of obtaining a sum greater than 9 , given that the black die resulted in a (b) Find the conditional probability of obtaining the sum 8 , given that the red die resulted in a number less than Solution:Assuming: B denote black coloured die and R denote red coloured die. Therefore, the sample space for the specified experiment will be as follows:...

### Mother, father and son line up at random for a family picture E: son on one end, F: father in middle

Solution: We assume that $\mathrm{M}$ denote mother, $\mathrm{F}$ denote father and $\mathrm{S}$ denote son. Then, the sample space for the given experiment will be: S= { MFS, SFM, FSM, MSF, SMF,...

### Mother, father and son line up at random for a family picture E: son on one end, F: father in middle

Solution: We assume that $mathrm{M}$ denote mother, $mathrm{F}$ denote father and $mathrm{S}$ denote son. Then, the sample space for the given experiment will be: S= $\{$ MFS, SFM, FSM, MSF, SMF,...

### Mother, father and son line up at random for a family picture E: son on one end, F: father in middle

Solution: We assume that $\mathrm{M}$ denote mother, $\mathrm{F}$ denote father and $\mathrm{S}$ denote son. Then, the sample space for the given experiment will be: S= ${$MFS, SFM, FSM, MSF, SMF,...

### A die is thrown three times, E: 4 appears on the third toss, and 5 appears respectively on first two tosses.

In the sample space, there are 216 outcomes, with each element of the sample space having three entries and taking the form $(x, y, z)$ where $1 \leq x, y, z \leq 6$. Considering the event, E: 4...

### A die is thrown three times, E: 4 appears on the third toss, and 5 appears respectively on first two tosses.

Solution: In the sample space, there are 216 outcomes, with each element of the sample space having three entries and taking the form $(x, y, z)$ where $\1 leq x, y, z leq 6$. Considering the event,...

### A die is thrown three times, E: 4 appears on the third toss, and 5 appears respectively on first two tosses.

Solution: In the sample space, there are 216 outcomes, with each element of the sample space having three entries and taking the form $(x, y, z)$ where $1 \leq x, y, z \leq 6$. Considering the...

### Two coins are tossed once, where (i) E: tail appears on one coin, : one coin shows head (ii) E: no tail appears, F: no head appears

Solution: Determining the sample space of the given experiment is $\mathrm{S}=\{\mathrm{HH}, \mathrm{HT}, \mathrm{TH}, \Pi\}\}$ (i) Given that, E: tail appears on one coin And F: one coin shows head...

### Determine P (E|F) in: A coin is tossed three times, where (i) : head on third toss, : heads on first two tosses (ii) : at least two heads, : at most two heads (iii) : at most two tails, at least one tail

Solution: The sample space of the given experiment will be: S={HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} (i) Given that, E: head-on third toss And F: heads on first two tossesSo writing the sample...

### If and , find(i) (ii) (iii) P (A U B)
Solution:Given $\mathrm{P}(\mathrm{A})=0.8, \mathrm{P}(\mathrm{B})=0.5$ and $\mathrm{P}(\mathrm{B} \mid \mathrm{A})=0.4$ (i) By definition of conditional probability, we know that,...