Question

Consider the example of finding the probability of selecting a black card or a $6$ from a deck of $52$ cards.
A. $\dfrac{8}{{13}}$
B. $\dfrac{7}{{13}}$
C. $\dfrac{6}{{13}}$
D. None of these

Answer 1

Hint : Probability is the state of being probable and the extent to which something is likely to happen in the particular situations or the favourable outcomes. Probability of any given event is equal to the ratio of the favourable outcomes with the total number of the outcomes.
Here, we would be using the formulas of probability of event to happen
$P(A) =$ Number of favourable or possible outcomes/ Total Number of outcomes

Complete step by step solution:
Given that, Shuffled deck $= 52$ cards
Therefore, Total Number of outcomes $= 52$
Now, the number of back cards $= 26$ (Which includes two cards with the number six and excluding the spades and clubs)
There are two cards with number six in those of heart and diamonds
Therefore, the required probability of drawing a black card or the number six is
$P(A) = \dfrac{{26 + 2}}{{52}}$
Simplify the above expression –
$P(A) = \dfrac{{28}}{{52}}$
Find the factors for the term on the right hand side of the above expression.
$P(A) = \dfrac{{7 \times 4}}{{13 \times 4}}$
Common multiple from the numerator and the denominator cancels each other. Therefore, remove from the numerator and the denominator
$P(A) = \dfrac{7}{{13}}$
This is the required solution.
So, the correct answer is “ $P(A) = \dfrac{7}{{13}}$”.

Note: The probability of any event always ranges between zero and one. It can never be the negative number or the number greater than one. The probability of impossible events is always equal to zero whereas, the probability of the sure event is always equal to one.