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Question

Three coins are tossed simultaneously. Arrange the given events in increasing order of their probabilities.

A
1 head
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B
At least 2 heads
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C
3 heads
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D
Atmost 2 heads
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Solution

When three coins are tossed, the sample space is given by:

S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}
n(S) = 8
1) Getting 1 head:
Favorable outcomes = {HTT, THT, TTH}
Probability of getting 1 head =Number of favorable outcomesTotal number of outcomes=38
2) Getting 3 heads:
Favorable outcomes = {HHH}
Probability of getting 3 heads =Number of favorable outcomesTotal number of outcomes=18
3) At least 2 heads:
Favorable Outcomes = {HHT, HTH, THH, HHH}
Number of favorable outcomesTotal number of outcomes=48
4) Atmost 2 heads
Favorable Outcomes = {HHT, HTH, HTT, THH, THT, TTH, TTT}
Number of favorable outcomesTotal number of outcomes=78

18<38<48<78

Increasing order of their probabilities: Getting 3 heads, Getting 1 head, At least 2 heads, Atmost 2 heads


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