An experiment consists of tossing a coin and then throwing it second time if a head occurs. If a tail occurs on the first toss, then a die is rolled once. Find the sample space.
A coin has two faces: head $(H)$ and tail $(T)$.
A die has six faces that are numbered from $1$ to $6,$ with one number on each face.
Thus, in the given experiment, the sample space is given by
$S =\{ HH , \,HT , \,T1, \,T2, \,T3,\, T4, \,T5,\, T 6\}$
Two dice are thrown simultaneously. The probability of getting the sum $2$ or $8$ or $12$ is
What is the probability that when one die is thrown, the number appearing on top is even
An anti aircraft gun take four shots at an enemy plane moving away from it. The probability of hitting the plane at the first, second, third and fourth shot are $0.4, 0.3, 0.2$ and $0.1$ respectively. The probability that the gun hit the plane is :-
A die is thrown. Describe the following events : $A$ : a number less than $7.$ , $B:$ a number greater than $7.$ Find the $A \cap B$
Four coins are tossed. The probability that at least one head turns up, is