A card is drawn at random from a well shuffled deck of 52 cards. If face cards are removed , then what is the probability of 1)Not getting an ace and 2) Getting a red numbered card greater than 7.
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Answers
Given :
A card is drawn at random from a well shuffled deck of 52 cards. Face cards are removed.
To Find :
- Not getting an ace
- Getting a red numbered card greater than 7
Required Formula :
P(E) = Favourable outcomes/Total no of outcomes
Explanation :
First let's understand!!
It is said that a deck of 52 playing cards is taken. But from that all face cards are removed.
We know that,
King, Queen and Jack are known as Face cards.
And we have four group of cards.
- Hearts
- Diamonds
- Clubs
- Spades
So each group is having 3 face cards.
- Total no of face cards = 4 × 3 = 12 face cards
It is said that face cards are removed.
After removing,
The cards = 52 - 12 = 40 cards
Finally,
∴ Total no of cards = 40 cards.
- Total Outcomes = 40
i) Not getting an ace :
We know that in a pack we have total 4 ace cards.
So,
- Favourable outcomes = 4
- Total outcomes = 40
Substituting the values,
⇒ P(an ace) = 4/40
⇒ P(an ace) = 1/10
∴ P(an ace) = 1/10
Now,
P(not an event) = 1 - P(an event)
⇒ P(not an ace) = 1 - 1/10
⇒ P(not an ace) = (10 - 1)/10
⇒ P(not an ace) = 9/10
∴ P(not an ace) = 9/10.
Probability of not getting an ace is 9/10.
ii) Getting a red numbered card greater than 7 :
We know that a pack is having 26 red cards.
The red cards are :
- Hearts
- Diamonds
The numbered cards are :
10, 9, 8, 7, 6, 5, 4, 3, 2.
Nos > 7 are :
- 8, 9, 10
So,
Numbers of red numbered cards > 7 = 2 × 3 = 6
- Favourable outcomes = 6
- Total outcomes = 40
Substituting the values,
⇒ P(red card > 7) = 6/40
⇒ P(red card > 7) = 3/20
∴ P(red card > 7) = 3/20.