 Hello and welcome to the session. The given question says a card is drawn at random from a well-shuffled deck of playing cards Find the probability that the card drawn is first a card of a spade or an ace second a king card Third neither a king nor a queen and fourth is either a king or a queen So let's start with the proof solution Now we know that what the number of cards in a well-shuffled deck is equal to 52 in a deck number of First let us denote by K R4 out of which to our red and to our black It's the late thing then the number of spade cards Let us denote the spade card bar is is equal to 13 and The number of ace cards denoting it by capital A is also four and the number of Queens Denoting it by Q is also equal to four Now we know that for an event a Probability of event a is equal to the number of favorable outcomes to the event a divided by the total number of possible outcomes therefore probability of drawing a king card is four divided by 52 this is equal to one divided by 13 and Let us denote the red king card by K Then there are two red king cards Therefore probability of drawing a red king will be equal to two divided by 52, which is equal to one divided by 26 and Probability of drawing a spade card is 13 divided by 52 on simplifying we get one divided by four Probability of drawing an ace card is four divided by 52 This is again equal to one divided by 13, which is equal to the probability of drawing a king card and probability of drawing a Queen card is also four divided by 52, which is equal to one divided by 13 So with the help of these probabilities, let us find the required one first we have to find Probability of drawing a spade or an ace card So this is equal to probability of s plus probability of a Which is equal to Probability of drawing a spade card is one divided by four and probability of drawing an ace card is one divided by 13 LCM of 4 and 13 is 52 and in the numerator we have 13 plus 4 which is equal to 17 divided by 52 Hence answer to the first part is 17 divided by 52 Now let's proceed on to the second part The second part we have to find the probability of drawing a red King card now there are four king cards as we have discussed earlier out of which two are read Therefore, we have two divided by 52 Which is equal to one divided by 26 So answer to the second part as one divided by 26 Now in the third part we have to find the probability that neither a king nor a queen card is drawn that is we have to find the probability of k complement and Q complement so this is equal to one minus probability of drawing a king Or a queen card So this is equal to one minus probability of drawing a King card plus probability of drawing a wind card This is further equal to one minus probability of drawing a king Is 4 divided by 52 And also probability of drawing a queen is also 4 divided by 52 so we have 52 minus 8 divided by 52 which is equal to 44 divided by 52 and this on further simplifying gives 11 divided by 13 So answer to the third part as 11 divided by 13 now proceeding on to the last part and which we have to find the probability of drawing either a king or a queen or a Queen so this is equal to probability of king plus probability of queen Which is equal to 4 divided by 52 Plus 4 divided by 52 and this is equal to 8 divided by 52 On simplifying we have 4 to the 8 4 into 13 is 52 So this is equal to 2 divided by 13 and on hence answer to the last part as 2 divided by 13 so this completes the session buy and take care