please answer this question
this question from probability chapter.
Answers
( i ) When a card is selected, the outcome can be any one of the 52 cards.
The set of all possible outcomes is called as the sample space and is denoted by S. So n(S) = 52.
The desirable event E is drawing an ace or picture card. There are 4 aces as also 4 kings, 4 queens and 4 jacks. E has , therefore, sixteen outcomes. So, n(E) = 16.
The probability of a desired event is defined as the ratio of number of outcomes favourable to it TO the number of all possible outcomes. Hence the required probability = n(E)/n(S) = 16/52 = 4/13.
( ii ) Probability = no of desirable outcomes / total number of outcomes
Total outcome = 52 ( 52 different cards in a deck )
desirable outcomes = Red cards + face cards - ( red and face cards )
Red Cards = 26
face cards = 3*4 = 12 ( I:e Jack , Queen , King in all 4 suits )
Red and Face = 6 ( Jack, Queen , King in Red )
Prob = (26 + 12 - 6 )/(52)
Prob = 32/52 = 8/13
( iii ) The 52 cards are 13 ranks in 4 suits, and there are therefore 4 kings and 4 queens in the deck. This means that there are 52 - 8 = 44 cards meeting that criterion, and the desired probability would then be
4452 = 1113 ≈ 84.6 %.
The odds associated with this would be 11 to 2 (5.5:1) in favor.
( iv ) There are 3 face cards in each suit
∴ There are 6 red face cards in all red cards
Total number of possible outcomes=26
P (red face card) = 6/26 = 3/13
( v ) Let A be the event in which the card drawn is an ace of spades
Accordingly n(A)=1. Since there is only one ace of spade in the deck.
∴P(A)=
Number of outcomes favourable to A / Total number of possible outcomes
= n ( A ) / n ( S )
= 1/52
( vi) The number of playing cards =52
Once card is drawn
Non-face and of red colour =13+3=16
Therefore,
Probability P(E)=16/52
=4/13
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