Hi everyone, could you please help me with these probability questions below.
. The Boston Bruins play in the Northwest Division of the Eastern
Confer-
ence in the National Hockey League. For each game played against
another
team in the Eastern Conference, the division[Atlantic(A), Northeast(N), or
Southeast(S)] and the outcome[win(W), loss(L), tie(T), or overtime loss(O)]
are recorded. Consider the following events.
E = The opponent is in the Southeast Division.
F = The Bruins win the game.
G = The opponent is in the Northeast or the game is an overtime loss.
H = The Bruins lose and the opponent is from the Atlantic Division.
a. Carefully
sketch a tree diagram to illustrate the possible outcomes for this experiment.
b. Find the sample space for this experiment.
c. Find the outcomes in each of the events E, F, G and H.
d. List the outcomes in E U F,F U G and H'
e. List the outcomes in E U H', E U F U G' and F U G' and F U G'
2. The germination rate for the pumpkin seeds is directly related to the prevaling weather conditions. The Autumn Gold Pumpkin is
medium-sized and ripens to a deep orange. If conditions are seasonable, the probability of
germination is 0.85. If it is dry, suppose the probability that a random seed will germinate is 0.75. Recent weather history suggests
there is a 40% chance of a dry start to the growing season. Suppose an Autumn Gold pumpkin seed is randomly selected.
a. What is the probability that the growing season will be dry and the seed will germinate?
b. What is the probability that the seed will germinate?
c. Suppose the seed did not germinate. What is the probability that thegrowing season had a dry start?
3. Customers at a Safeway grocery store in Scottsdale, Arisona can pay forpurchases with cash, an ATM card, or a credit card. Fifty-ve percent of
all customers use cash and 38% use an ATM card. Careful research has shown thatof those paying with cash, 75% use coupons; of those using an ATM card, 35%
use coupons; and of those using a credit card, only 10% use coupons. Suppose
a customer is randomly selected.
a. What is the probability that
the customer pays with a credit card and
does not use coupons?
b. What is
the probability that the customer does not use coupons?
c. If the customer
does not use coupons, what is the probability that he or
she paid with an ATM
card?
4. While the temperature range of most household ovens is
approximately
200-600 oF, most customers only use four or ve common setting.
Suppose the
1
probability distribution for the oven temperature setting
for a random selected
use is given in the table below.
x 300 325 350 375
400 500
p(x) 0.04 0.205 0.40 0.075 0.20 0.08
a. Find the mean, variance,
and standard deviation of the oven temperature
settings.
b. Suppose three
dierent uses are randomly selected. Find the probability
that the
temperature settings for all three are at least 400 oF.
c. Supppose three
dierent uses are randomly selected. Find the probability
that exactly one
use is for 350 oF.
5. A commuter train from Long Island to New York City is
scheduled to
arrive at 8:07 A.M. every weekday morning. The probability that
the train
arrives on time is 0.90. Suppose 20 weekdays are randomly
selected.
a. Find the probability that the train will arrive on time on at
most 15 days.
b. Find the probability that the train will arrive on time on
at least 12 days.
c. Find the expected number of days that the train will
arrive on time.
d. Suppose the train arrives on time on at least 15 days.
What is the
probability that it arrives on time on all 20 days?