When tossing 3 coins simultaneously, X represents the number of heads obtained.
The condition 0<X<3 means X is more than 0 and less than 3, so X can be either 1 or 2.
When 3 coins are tossed, each coin can be either Head (H) or Tail (T).
Total possible outcomes =2×2×2=8
The complete list of outcomes with their corresponding number of heads:
HHH: 3 heads
HHT: 2 heads
HTH: 2 heads
HTT: 1 head
THH: 2 heads
THT: 1 head
TTH: 1 head
TTT: 0 heads
For 0<X<3, we need X = 1 or X = 2.
Outcomes where X = 1: HTT, THT, TTH (3 outcomes)
Outcomes where X = 2: HHT, HTH, THH (3 outcomes)
Total favorable outcomes =3+3=6
P(0<X<3)=Total outcomesFavorable outcomes
P(0<X<3)=86
P(0<X<3)=43
Therefore, P(0<X<3)=43