Question

“A” draws two cards with replacement from a pack of $52$ cards and “B” throws a pair of dice. What is the chance that “A” gets both cards of same suit and “B” gets total of $6$
$A)\dfrac{1}{{144}}$
$B)\dfrac{1}{4}$
$C)\dfrac{5}{{144}}$
$D)\dfrac{7}{{144}}$

Answer 1

Probability is the term mathematically with events that occur, which is the number of favorable events that divides the total number of the outcomes. In the question, we ask to find the chances which means the probability.
There are a total $52$ cards in a deck of cards. In the $52$ cards, there are spades, hearts, diamonds, and clubs which each contain $13$ cards.
In a dice, there are six sides, and a pair of dice means two dice which means total $36$ possible ways.
Formula used:
$P = \dfrac{F}{T}$where P is the overall probability, F is the possible favorable events and T is the total outcomes from the given

Complete step-by-step solution:
Since from the given that we have, “A” draws two cards with replacement from a pack of $52$ cards.
Since the requirement is to find the probability of both cards of the same suit. Same suits mean same numbers (identical)
Since each of these four shapes contains $A,2,3,...,10,J,Q,K$ respectively.
Hence the possible ways to get the same cards are $13$ (there are thirteen in every four shapes and thus we get the identical cards)
$P = \dfrac{F}{T} = \dfrac{{13}}{{52}} = \dfrac{1}{4}$
Similarly, the “B” throws a pair of dice, and “B” gets a total of $6$
Since dice have six sides, which are $1,2,3,4,5,6$ and the second dice also having the same numbers.
Hence the pair of dice having gets total of $6$ are $(1,5),(2,4),(3,3),(4,2),(5,1)$ (total means, in addition, we need number six), we have five events.
Hence, we get $P = \dfrac{F}{T} = \dfrac{5}{{36}}$
Thus, the chance that “A” gets both cards of the same suit and “B” gets a total of $6$ is $\dfrac{1}{4} \times \dfrac{5}{{36}} = \dfrac{5}{{144}}$
Therefore, the option $C)\dfrac{5}{{144}}$ is correct.

Note: If we divide the probability and then multiplied with the hundred then we will determine its percentage value.
Like take $\dfrac{5}{{144}} = 0.034$ then multiplied with the number $100$ then we get $0.034 \times 100 = 3.4\%$ is the chance that “A” gets both cards of the same suit and “B” gets a total of $6$
$\dfrac{1}{6}$which means the favorable event is $1$ and the total outcome is $6$
Since the total outcome of cards is $52$ and a pair of dice is $6 \times 6 = 36$.