3. 3 unbiased coins are tossed examples
1) 3 unbiased coins are tossed. What is the probability of getting atmost 2 Tail
Solution:
Total number of outcomes possible when a coin is tossed`=2`
Hence, total number of outcomes possible when `3` coins are tossed,
`:.n(S)=2 xx 2 xx 2=8`
Here `S` = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
Let `E` = event of getting atmost `2` tail
`:.` `E` = {HHH, HHT, HTH, HTT, THH, THT, TTH}
`:.n(E) = 7`
`:.P(E)=(n(E))/(n(S))=7/8`
2) 3 unbiased coins are tossed. What is the probability of getting atleast 2 Tail
Solution:
Total number of outcomes possible when a coin is tossed`=2`
Hence, total number of outcomes possible when `3` coins are tossed,
`:.n(S)=2 xx 2 xx 2=8`
Here `S` = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
Let `E` = event of getting atleast `2` tail
`:.` `E` = {HTT, THT, TTH, TTT}
`:.n(E) = 4`
`:.P(E)=(n(E))/(n(S))=4/8=1/2`
3) 3 unbiased coins are tossed. What is the probability of getting exactly 2 Head
Solution:
Total number of outcomes possible when a coin is tossed`=2`
Hence, total number of outcomes possible when `3` coins are tossed,
`:.n(S)=2 xx 2 xx 2=8`
Here `S` = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
Let `E` = event of getting exactly `2` head
`:.` `E` = {HHT, HTH, THH}
`:.n(E) = 3`
`:.P(E)=(n(E))/(n(S))=3/8`
4) 3 unbiased coins are tossed. What is the probability of getting atleast 1 Head
Solution:
Total number of outcomes possible when a coin is tossed`=2`
Hence, total number of outcomes possible when `3` coins are tossed,
`:.n(S)=2 xx 2 xx 2=8`
Here `S` = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
Let `E` = event of getting atleast `1` head
`:.` `E` = {HHH, HHT, HTH, HTT, THH, THT, TTH}
`:.n(E) = 7`
`:.P(E)=(n(E))/(n(S))=7/8`
This material is intended as a summary. Use your textbook for detail explanation.
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