If the probability that a vaccine you took will protect you from getting the flu
ID: 3300820 • Letter: I
Question
If the probability that a vaccine you took will protect you from getting the flu is 0.965, what is the probability that you will get the flu? If there is a 1 in 1,000 chance that you will pick the numbers correctly in tonight's lottery, what is the probability that you will not pick the numbers correctly? If there is a 1 in 4 chance that it will rain for your Fourth of July barbecue, what is the probability that it won't rain? If two dice are rolled, find the probability that neither die shows a five on it. If two dice are rolled, find the probability that the total showing is less than 10. If five coins are flipped, what is the probability of obtaining at least one head? If five coins are flipped, what is the probability of obtaining at least one head and at least one tail?Explanation / Answer
6.
Let (a,b) denote a possible outcome of rolling 2 dice. Since a and b can take values 1.2.3.4.5.6, when 2 dice are rolled, total possibilities are 36.
Possible outcomes with total less than 10 are:
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6) - 6 Nos
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6) - 6 Nos.
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6) - 6 Nos
(4,1), (4,2), (4,3), (4,4), (4,5) - 5 Nos
(5,1), (5,2), (5,3), (5,4) - 4 Nos
(6,1), (6,2), (6,3) - 3 Nos.
Total possibilies of total tess than 10 are = 30
So, Required probability = 30/36 = 0.8333
8.
Given:
5 coins are flipped.
Total 25 = 32 possibilities.
At least 1 Head & 1 Tail are:
H H H H T 1
H H H T H 2
H H H T T 3
H H T H H 4
H H T H T 5
H H T T H 6
H H T T T 7
H T H H H 8
H T H H T 9
H T H T H 10
H T H T T 11
H T T H H 12
H T T H T 13
H T T T H 14
H T T T T 15
T H H H H 16
T H H H T 17
T H H T H 18
T H H T T 19
T H T H H 20
T H T H T 21
T H T T H 22
T H T T T 23
T T H H H 24
T T H H T 25
T T H T H 26
T T H T T 27
T T T H H 28
T T T H T 29
T T T T H 30
So,
Probability of obtaining at least one head and at least one tail = 30/32 = 0.9375