Question

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

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

Answer 1

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

S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}
$\Rightarrow$ n(S) = 8
1) Getting 1 head:
Favorable outcomes = {HTT, THT, TTH}
Probability of getting 1 head =$\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{3}{8}$
2) Getting 3 heads:
Favorable outcomes = {HHH}
Probability of getting 3 heads =$\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{1}{8}$
3) At least 2 heads:
Favorable Outcomes = {HHT, HTH, THH, HHH}
$\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{4}{8}$
4) Atmost 2 heads
Favorable Outcomes = {HHT, HTH, HTT, THH, THT, TTH, TTT}
$\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{7}{8}$

$\frac{1}{8}<\frac{3}{8}<\frac{4}{8}<\frac{7}{8}$

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