Respuesta :
a) P(Club) = 1/6
b) P(red card) = 13/30
c) P(not a heart) = 9/10
What is probability?
"Probability is a branch of mathematics which deals with finding out the likelihood of the occurrence of an event."
The formula of the probability of an event A is:
P(A) = n(A) / n(S)
where, n(A) is the number of favorable outcomes and n(S) is the total number of events in the sample space.
For given situation,
A card was drawn at random 30 times.
⇒ n(S) = 3
a) To find: P(club)
The frequency of getting club card = 5
⇒ n(club) = 5
So, the probability of getting club card would be,
P(club) = n(club)/n(S)
⇒P(club) = 5/30
⇒ P(club) = 1/6
So, the experimental probability of getting club is 1/6.
As there are 13 club cards in the standard deck of 52 cards, the theoretical probability of getting club is 13/52 i.e., 1/4
This means for getting or selecting club card,
theoretical probability > experimental probability because 1/4 > 1/6
b) To find : P(red card)
The heart and diamond card are the red cards.
The frequency of getting red card = frequency of getting heart card + frequency of getting diamond card
= 3 +10
= 13
⇒ n(red card) = 13
So, from given experiment the probability of getting club card would be,
P(red card) = n(red card)/n(S)
⇒P(red card) = 13/30
⇒ P(red card) = 0.433
So, the experimental probability of getting red cards is 0.4333
As there are 26 red cards in the standard deck of 52 cards, the theoretical probability of getting red cards is:
= 26/52
= 1/2
= 0.5
> 0.433
This means for getting or selecting red cards,
theoretical probability > experimental probability
c) To find: P(not a heart)
i.e., to find P(Diamond or Club or Spade)
P(Diamond or Club or Spade)
= P(Diamond) + P(Club) + P(Spade)
= n(Diamond)/n(S) + n(Club)/n(S) + n(Spade)/n(S)
= (10/30) + (5/30) + (12/30)
= 27/30
= 9/10
= 0.9 ..........................(1)
This means, P(not a heart) = 9/10
Theoretically, probability of getting heart is 13/52 i.e., 0.25
This means, the probability of getting no heart would be,
1 - 0.25 = 0.75 ........................(2)
So, the theoretical probability of not a heart = 0.75
From (1) and (2), for an event 'not a heart'
experimental probability > theoretical probability
Learn more about probability here:
brainly.com/question/12478394
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