Could I get help with these probabilities Is there a standar

3) What is the probability that we will draw a spade from a deck of cand (standand 53can deck)? Orn 3a) What is the probability that we will draw and ace from a deck of cards? PL a spade card): 0.0749 5a 3b) What is the probability that we will draw the ace of spades from a deck of cards? of-Spades is13 3c) What is the probability that we will draw a jack or a king from a deck of cards? d) What is the probability that we will draw and jack and a king with two draws? 3e) What i draws? is the probability we will draw the ace of spades and the king of hearts with two 4) If a standard normal distribution has a mean of 150 and a standard deviation of 5, what is the probability that we will draw a z-score of 1.96 or higher? (think about this one) 4a) Using the information above, what z-score would be greater than9% of all of the other scores? 5) What is the sampling distribution of the mean? What 3 attributes of this distribution are inferred from the central limit theorem? 6) What is a z score and what is it used for?

Solution

Sure, you will get help on probability problems.   

There are some standard formula on probability.

Suppose we have event E and total number of all possible distinct outcomes S.

i.e. n(E) and n (S)

then P(E) = Total number of favourable outcomes to event E / All possible distinct outcomes in sample space.

= n(E) / n(S)

Suppose we roll die is an experiment:

then Total number of all possible distinct outcomes S = { 1 , 2 , 3 , 4 , 5 , 6 }

i.e. n(S) = 6

Consider event E= {2 , 4 , 6 } i.e. n (E) = 3

Therefore, P(E) = 3 / 6 = 1 /2

Lets solve for your question now.

3 solution: P{ We will draw spade cards from deck of 52 } = 13 /52

Since we need to draw only one card from standard deck of 52.

Therefore, n(S) = C(52 , 1 ) = 52 and Total spade cards in deck are = 13 so, n(E) = C(13 , 1 ) = 13

3a) Solution: The probability of drawing a specific number (or specific face card) is = 4/52

Total number of ace cards are = 4

draw one card from 4 means C(4 , 1 ) = 4

3b) solution : P[ we will draw ace of spade cards]

ace of spade card in deck of 52 is only 1

So select one from 1 spade card is C(1 , 1 ) = 1

Therefore,   P[ we will draw ace of spade cards] = 1 /52

The probability of drawing a specific card is ¹/₅₂.

3c) Solution : P[a king or a jack}

Total number of king is 4 out of 52 cards.

Total number of jack is 4 out of 52 cards

Number of favourable outcomes i.e. ‘a king or a jack’ is 4 + 4 = 8 out of 52 cards.

Therefore, probability of getting ‘a king or a jack’

   Number of favorable outcomes
^{P(E) =}   Total number of possible outcome

= 8/52
= 2/13

3d) solution : From a standard deck of cards, one card is drawn. What is the probability that the card is jack and a
king? P( Jack and king ) = (4/52)*(4/52) = 1/169 ...........................(It is for first draw)

from second draw we have only 51 cards.

there may be 4 jack and 4 king cards.

P( jack and king ) = (4/51)(4/51) = 16/2601

You can solve for 3e in same way.

number of ace of spade = 1 and number of king of heart = 1

for first draw P [ We will draw ace of spade and king of heart ] = (1/52)(1/52) = 1/2704

for second draw we have only 51 cards therefore,

P [ We will draw ace of spade and king of heart ] = (1/51)(1/51) = 1/2601 -----------------------( for second draw)