What is the probability that a) A card chosen from an ordinary deck of 52 cards is an ace? b) A randomly selected integer chosen from the first 100 positive integers is odd? c) A randomly selected day of the year 2020 is in May? d) The sum of the numbers on two dice is even when they are rolled? e) A fair coin lands Heads 6 times in a row? f) A fair coin lands Heads 4 times out of 5 flips? g) The bit string has exactly two 1s, given that the string begins with a 1 if you pick a bit string from the set of all bit strings of length ten? h) The bit string has the sum of its digits equal to seven if you pick a bit string from the set of all bit strings of length ten?

a) 0.076

b) 0.5

c) 0.084

d) 0.25

e) 0.00024

f) 0.156

Step-by-step explanation:

a) In an ordinary deck there are 4 aces. The probability of getting an ace is given by:

n: options for an ace = 4

N: total number of cards = 52

The probability is 7.6%

b) On the first 100 positive integers, there are 50 odd integer numbers. Then you have:

The probability of getting an odd number is 50%

c) From a total of 365 day in the year, May has 31 day. Then you have:

The probability is 8.4%

d) In this case you have two events. To get an odd number with the sum of the number of two dices you need and odd number in one dice and a pair number in the other dice.

The probability is the product of the occurrence of both events. The probability for an odd number is 1/2 and for a pair number is 1/2.

The probability is 25%

e) To obtain Head 6 times in a row, the probability is:

Probability of 0.024%

f) To get Head 4 times from 5 flights, you first calculate the probability for 1 head in five flips:

There are 5 forms of getting 4 Heads for 5 flips, then you have:

Te probability is 15.6%

correct choice is b

step-by-step explanation:

when you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. for the function the average rate of change from point to point can be calculated as

to find the average rate of change from day 2 to day 10, note that at day 2, 8 houses were sold, so a(2,8) and at day 10, 2 houses were sold, so b(10,2). thus,