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 box contains $3$ white and $2$ red balls. A ball is drawn and another ball is drawn without replacing first ball, then the probability of second ball to be red is
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Three persons work independently on a problem. If the respective probabilities that they will solve it are $\frac{{1}}{{3}} , \frac{{1}}{{4}}$ and $\frac{{1}}{{5}}$, then the probability that none can solve it
One card is drawn from a well shuffled deck of $52$ cards. If each outcome is equally likely, calculate the probability that the card will be a black card (i.e., a club or, a spade)
If the lengths of the sides of a triangle are decided by the three throws of a single fair die, then the probability that the triangle is of maximum area given that it is an isosceles triangle, is