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 $P \left( B ^{\prime}\right)=1- P ( B )=1-\frac{4}{52}=1-\frac{1}{13}=\frac{12}{13}$
In a single throw of two dice, the probability of obtaining a total of $7$ or $9$, is
An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events:
$A:$ the sum is greater than $8$,
$B : 2$ occurs on either die
$C:$ the sum is at least $ 7$ and a multiple of $3.$
Which pairs of these events are mutually exclusive ?
If $A$ is a sure event, then the value of $P (A$ not ) is
From a pack of $52$ cards two cards are drawn in succession one by one without replacement. The probability that both are aces is
Let $A, B, C$ be three mutually independent events. Consider the two statements ${S_1}$ and ${S_2}$
${S_1}\,\,:\,\,A$ and $B \cup C$ are independent
${S_2}\,\,:\,\,A$ and $B \cap C$ are independent
Then