Question

If a coin is tossed three times, find probability of getting

1) Exactly 3 tails
2) Atmost 2 heads
3) Atleast 2 tails
4) Exactly 2 heads
5) Exactly 3 heads​

Answer 1

`{\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}`

‣ A coin is tossed three times.

`{\large{\textsf{\textbf{\underline{\underline{To \: Find :}}}}}}`

‣ The probability of getting,

1) Exactly 3 tails

2) At most 2 heads

3) At least 2 tails

4) Exactly 2 heads

5) Exactly 3 heads

`{\large{\textsf{\textbf{\underline{\underline{Using \: Formula :}}}}}}`

`\star \: \tt P(E)= {\underline{\boxed{\sf{\red{ ( Favourable \: outcomes )/(Total \: outcomes) }}}}}`

`{\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}`

★ When three coins are tossed,

then the sample space = {HHH, HHT, THH, TTH, HTH, HTT, THT, TTT}

[here H denotes head and T denotes tail]

⇒Total number of outcomes
`\tt [ \: n(s) \: ]` = 8

1) Exactly 3 tails

Here

• Favourable outcomes = {HHH} = 1

• Total outcomes = 8

`\therefore \sf Probability_((exactly \: 3 \: tails)) = \red{ (1)/(8)}`

2) At most 2 heads

[It means there can be two or one or no heads]

Here

• Favourable outcomes = {HHT, THH, HTH, TTH, HTT, THT, TTT} = 7

• Total outcomes = 8

`\therefore \sf Probability_((at \: most \: 2 \: heads)) = \green{ (7)/(8)}`

3) At least 2 tails

[It means there can be two or more tails]

Here

• Favourable outcomes = {TTH, TTT, HTT, THT} = 4

• Total outcomes = 8

`\longrightarrow \sf Probability_((at \: least \: 2 \: tails)) = (4)/(8)`

`\therefore \sf Probability_((at \: least \: 2 \: tails)) = \orange{(1)/(2)}`

4) Exactly 2 heads

Here

• Favourable outcomes = {HTH, THH, HHT } = 3

• Total outcomes = 8

`\therefore \sf Probability_((exactly \: 2 \: heads)) = \pink{ (3)/(8)}`

5) Exactly 3 heads

Here

• Favourable outcomes = {HHH} = 1

• Total outcomes = 8

`\therefore \sf Probability_((exactly \: 3 \: heads)) = \purple{ (1)/(8)}`

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