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 diamond not an ace
When a card is drawn from a well shuffled deck of $52$ cards, the number of possible outcomes is $52$
We assume that the event 'Card drawn is an ace' is $B.$
Therefore Card drawn is not an ace' should be $B ^{\prime}$
We know that $P \left( B ^{\prime}\right)=1- P ( B )=1-\frac{4}{52}=1-\frac{1}{13}=\frac{12}{13}$
A six faced dice is so biased that it is twice as likely to show an even number as an odd number when thrown. It is thrown twice. The probability that the sum of two numbers thrown is even, is
Let $\mathrm{X}$ and $\mathrm{Y}$ be two events such that $\mathrm{P}(\mathrm{X})=\frac{1}{3}, \mathrm{P}(\mathrm{X} \mid \mathrm{Y})=\frac{1}{2}$ and $\mathrm{P}(\mathrm{Y} \mid \mathrm{X})=\frac{2}{5}$. Then
$[A]$ $\mathrm{P}\left(\mathrm{X}^{\prime} \mid \mathrm{Y}\right)=\frac{1}{2}$ $[B]$ $\mathrm{P}(\mathrm{X} \cap \mathrm{Y})=\frac{1}{5}$ $[C]$ $\mathrm{P}(\mathrm{X} \cup \mathrm{Y})=\frac{2}{5}$ $[D]$ $\mathrm{P}(\mathrm{Y})=\frac{4}{15}$
From a pack of $52$ cards two cards are drawn in succession one by one without replacement. The probability that both are aces is
The probability of India winning a test match against West Indies is $\frac{1}{2}$. Assuming independence from match to match, the probability that in a $5$ match series India's second win occurs at the third test, is
In each of the following experiments specify appropriate sample space A boy has a $1$ rupee coin, a $2$ rupee coin and a $5$ rupee coin in his pocket. He takes out two coins out of his pocket, one after the other.