PSY 555 Homework 9

5.14.                       p(that any applicant will be admitted)=the ratio of the number admitted to the number applying=10/300=.03.

There is a  probability that a person in the top 20% will be admitted using this procedure.

5.21.      Plot of correct choices on trial 1 of a 5-choice task.

5.23.                       p(5 or more correct)=p(5)+p(6)+p(7)+p(8)+p(9)+p(10) =.0264+.0055+.0008+.0001+.0000+.0000=.028.

Assuming that the alpha level we use is equal to .05, four choices (with a probability of .0881) still falls within chance levels.  The probability of five people making correct choices is .028, which falls below the .05 alpha level.  So, it is relatively safe to conclude that five correct choices for the first trial indicates subjects are performing above chance levels.

5.26.                       Number of subjects needed in verbal learning experiment if each is to see different classes of words in a different order.

We would need 24 subjects—1 for each of the 24 possible permutations.

5.29.                       The total number of ways of making ice cream cones=

They can truthfully advertise that they have 63 different combinations.

5.30.                       Different ways to record from the rat’s brain:

There are 15 ways to record from the brain.

1.                                      Permutations are all the possible orderings of variable elements.

An example of a permutation would be trying to decide all the permutations of 4 posters to displayed on a museum wall, if only two posters can be on the wall at any given time.

AB BA

AC CA

BC CD

BD DB

CD DC

Combinations are all the possible different pairings of variable elements (order does not matter for these).

An example of a combination would be the pairings of food for dinner plates at a buffet with 4 different types of food, if on each dinner plate you get to choose 3 items(assuming you don’t care what food is touching, i.e., order doesn’t matter).

Chicken,corn,potatoes

Apple,potatoes,corn

Corn,apple,chicken

Chicken,potatoes,apple

2.         N=10

r=7

There are 604,800 possible passwords he will need to try.

3.         Need to use the binomial distribution formula for this problem (0 to 3 plus 17 to 20)

4(a).      The answer depends on how you interpreted the question.  If you interpreted it as one of the first four cards that the dealer receives being a red joker, the probability is calculated as follows:

P[joker on first draw)=

P[joker on second draw)=

P[joker on third draw)=

P{joker on fourth draw)=

P[J+J+J+J]=

There is a .00000001334 probability that the first four cards that the dealer receives will all be red jokers.

If you interpreted the problem to mean the probability that all of the first four cards dealt out by the dealer being a red joker, then the probability is calculated as follows:

P[joker on first draw)=

P[joker on second draw)=

P[joker on third draw)=

P{joker on fourth draw)=

P[J+J+J+J]=

There is a .00000001134 probability that the first four cards that are dealt by the dealer will all be red jokers.

4(b).      The answer depends on how you interpreted the question.  If you interpreted it as one of the first five cards that the dealer receives being a red joker, the probability is calculated as follows:

P[joker on first draw)=

P[joker on second draw)=

P[joker on third draw)=

P{joker on fourth draw)=

P(joker on fifth draw)=

P[J or J or J or J or J]=

There is a .0981 probability that one of the dealer's first five cards drawn will be a red joker.

If you interpreted the problem to mean the probability that one of the first five cards dealt out by the dealer being a red joker, then the probability is calculated as follows:

P[joker on first draw)=

P[joker on second draw)=

P[joker on third draw)=

P{joker on fourth draw)=

P(joker on fifth draw)=

P[J or J or J or J or J]=

There is a .0935 probability that one of the first five cards dealt will be a red joker.

4(c).     The probability is 0 that each person will start the game with a red joker because there are five people and only four red jokers in the deck.

4(d).     Player 1—A,K,2,6,8,10,Jack

Player 2-Red Joker,9,3,5,4,Jack, Black Joker

Player 3-K,Q,3,6,9,10,Black Joker

Player 4-2,7,7,10,Q,K,A

Player 5-4,8,8,Jack,Red Joker,Q,7

Given this information, what is the probability that the next card drawn from the deck will be a 4?

216-35=181 card left in the deck

(4 fours)(4 decks)=16[4's]-2[4's]=Fourteen 4's left in the deck

P[4]=

There is a .0773 probability that the next card drawn from the deck will be a 4.