Describe the sample space for the indicated experiment: A coin is tossed and then a die is rolled only in case a head is shown on the coin.
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, when a coin is tossed and then a die is rolled only in case a head is shown on the coin. the sample space is given by:
$S =\{ H1, \,H 2,\, H 3,\, H 4, \,H 5, \,H 6,\, T \}$
A die is rolled. Let $E$ be the event "die shows $4$ " and $F$ be the event "die shows even number". Are $E$ and $F$ mutually exclusive ?
If a dice is thrown twice, then the probability of getting $1$ in the first throw only is
The probability that a marksman will hit a target is given as $1/5$. Then his probability of at least one hit in $10$ shots, is
A bag contains $3$ red and $7$ black balls, two balls are taken out at random, without replacement. If the first ball taken out is red, then what is the probability that the second taken out ball is also red
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 :-