Question

The chance of throwing an ace in the first only of two successive throws with an ordinary die is:
A.$\dfrac{1}{{36}}$
B.$\dfrac{5}{{36}}$
C.$\dfrac{{25}}{{36}}$
D.$\dfrac{1}{6}$

Answer 1

Hint: First, we will find the probability of getting an ace when die is thrown once. Now, we want an ace only on the first throw, so we will next find the probability of not getting an ace. To find the probability of throwing an ace in the first only of two successive throws with an ordinary die, we will multiply both the probabilities of first throw and the second throw.

Complete step-by-step answer:
We have to find the probability of throwing an ace in the first only of two successive throws in an ordinary die.
First, we will have the probability of throwing an ace on the first throw.
There are 6 numbers on a die, in which 1 appears only once.
That is, the number of favourable outcomes is 1 and the total possible outcome is 6.
We know that the probability is given as, $\dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Number of possible outcomes}}}}$
Hence, the probability of getting an ace in first throw is \[\dfrac{1}{6}\]
Now, we want a ace only on the first throw. hence, we do not 1 in the second throw.
That is, for the second throw there are 5 favourable outcomes out of 6 possible outcomes.
Hence, the probability of getting a number other than ace is $\dfrac{5}{6}$
Next, we will multiply both the probabilities of first and second throw to get the probability of throwing an ace in the first only of two successive throws in an ordinary die.
That is, $\dfrac{1}{6}\left( {\dfrac{5}{6}} \right) = \dfrac{5}{{36}}$
Hence, option B is correct.

Note: We can also do this question by writing the favourable outcomes. The outcomes where 1 comes only in first throw are $\left( {1,2} \right),\left( {1,3} \right),\left( {1,4} \right),\left( {1,5} \right),\left( {1,6} \right)$ . That is, there are 5 favourable outcomes. Whenever a dice is thrown twice, the possible number of outcomes are 36. Hence, the required probability is $\dfrac{5}{{36}}$